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|Chapter Name||Comparing Quantities|
NCERT Exemplar Class 7 Maths Chapter 7 Comparing Quantities Solutions
Multiple Choice Questions (MCQs)
20% of 700 m is
(a) 560 m (b) 70 m (c)210 m (d)140 m
(d) We have, 20% of 700 m = x 700 = 20 x 7 = 140 m
Hence, 20% of 700 m is 140 m.
Gayatri’s income is Rs 160000 per year. She pays 15% of this as house rent and 10% of the remainder on her child’s education. The money left with her is
(a) Rs 136000 (b) Rs 120000 (c) Rs 122400 (d) Rs 14000
(c) Income of Gayatri = ? 160000 [given]
Money paid as house rent = 15% of 160000 = x 160000 = Rs 24000
Remaining amount = 160000 – 24000 = Rs 136000
Money spent on child’s education = 10%of 136000 = x 136000 = Rs 13600
Money left with her = 136000 -13600= Rs 122400
The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money saved by her is
(a) 20% (b) 25% (c) 40% (d) 80%
(a) Given, ratio of income to savings = 4:1
0.07 is equal to
(a) 70% (b) 7%
(c) 0.7% (d) 0.07%
(b) We have, 0.07
In percentage, 0.07 =x100%=7%
Note: To convert any number into per cent, we multiply that number by 100 along with the symbol ‘%’
In a scout camp, 40% of the scouts were from Gujarat state and 20% of these were from Ahmedabad. The percentage of scouts in the camp from Ahmedabad is
(a) 25% (b) 32.5%
(c) 8% (d) 50%
(c) Let the scouts in scout camp = 100
What per cent of Rs 4500 is Rs 9000?
(a) 200% (b) 1/2%
(c) 2% (d) 50%
5.2 is equal to
(a) 52% (b) 5.2%
(c) 520% (d) 0.52%
(c) We have, 5.2
In percentage, x 100% = 520%
The ratio 3 : 8 is equal to
(a) 3.75% (b) 37.5% (c) 0.375% (d) 267%
(b) Given, ratio =3:8
In percentage, x 100% = 37.5%
225% is equal to
(a) 9 : 4 (b) 4 : 9 (c) 3 : 2 (d) 2 : 3
(a) We have, 225%
For fraction, 225 x
∴ Required ratio = 9:4
Note: The sign of percentage (%) is removed dividing the number by 100.
A bicycle is purchased for Rs 1800 and is sold at a profit of 12%. Its selling price is
(a) Rs 1584 (b) Rs 2016 (c) Rs 1788 (d) Rs 1812
(b) Given, cost price of bicycle = ? 1800 and profit =12%
As we know,
A cricket bat was purchased for Rs 800 and was sold for Rs 1600. Then, profit earned is
(a) 100% (b) 64% (c) 50% (d) 60%
A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the buffalo at a loss of 5% but made a profit of 10% on the cow. The net result of the transaction is
(a) loss of Rs 200 (b) profit of Rs 400
(c) loss of Rs 400 (d) profit of Rs 200
If Mohan’s income is 25% more than Raman’s income, then Raman’s income is less than Mohan’s income by
(a) 25% (b) 80%
(c) 20% (d) 75%
(c) Let the Raman’s income be x. it is given that Mohan’s income is 25% more than
The interest on t 30000 for 3 yr at the rate of 15% per annum is
(a) 7 4500 (b) 7 9000 (c) 7 18000 (d) 7 13500
Amount received on Rs 3000 for 2 yr at the rate of 11% per annum is
(a) Rs 2340 (b) Rs 3660 (c) Rs 4320 (d) Rs 3330
Interest on Rs 12000 for 1 month at the rate of 10% per annum is
(a) Rs 1200 (b) Rs 600 (c) Rs 100 (d) Rs 12100
Rajni and Mohini deposited Rs 3000 and Rs 4000 in a company at the rate of 10% per annum for 3 yr and yr, respectively. The difference of the amounts received by them will be
(a) Rs 100 (b) Rs 1000 (c) Rs 900 (d) Rs 1100
If 90% of x is 315 km, then the value of x is
(a) 325 km (b) 350 km (c) 405 km (d) 340 km
On selling an article for Rs 329, a dealer lost 6%. The cost price of the article is
(a) Rs 310.37 (b) Rs 348.74 (c) Rs 335 (d) Rs 350
The sum which will earn a simple interest of Rs 126 in 2 yr at 14% per annum, is
(a) Rs 394 (b) Rs 395 (c) Rs 450 (d) Rs 540
The per cent that represents the unshaded region in the figure, is
The per cent that represents the shaded region in the figure, is
Fill in the Blanks
In questions 24 to 59, fill in the blanks to make the statements true.
2 : 3=_____%
Given ratio = 2:3
In percentage=2/3 x 100%=%
30% of Rs 360 = ________
We have, 30% of Rs 360 = x 360 = Rs 108
120% of 50 km =___________
We have, 120% of 50 km = x 50 km = 60 km
We have, 2.5
In percentage, 2.5 x 100% = 250%
We have, 8/5
In percentage, 8/5 x 100% = 160%
A_____with its denominator 100 is called a per cent.
A fraction with its denominator 100 is called a per cent.
15 kg is____% of 50 kg.
Weight of Nikhil increased from 60 kg to 66 kg. Then, the increase in weight is_____%
We have, initial weight of Nikhil = 60 kg
After increase in weight, weight became =66 kg ‘ Increase in weight = 66 – 60 = 6 kg
∴ Increase percentage of weight
x100%= x100%= %=10%
So, the number of students present on that day, was 46.
In a class of 50 students 8% were absent on one day. The number of students present on that day, was______.
We have, total number of students =50 Absent on one day = 8%
Percentage of present students on that day = 100-8 = 92%
∴ Number of students present on that day = 92% of 50 = x 50 = = 46
So, the number of students present on that day, was 46.
Savitri obtained 440 marks out of 500 in an examination. She secured _____% marks in the examination.
Marks obtained by Savitri out of 500 = 440
Percentage of marks obtained = x 100% = 88%
Hence, Savitri secured 88% marks in the examination.
Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of the deposit. Now, the balance in her account is_____.
Total deposit=Rs 1500
Amount withdrawn = 40% of Rs 1500 = x 1500 = Rs 600
∴ Balance in the account = 1500 – 600 = Rs 900
____ is 50% more than 60.
Let number be x. It is given that x is 50% more than 60.
Therefore, x = 60 + 50% of 60 = 60 + x 60 = 60 + 30 = 90
John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat is___.
Given, SP of bat = Rs 75 and loss = Rs 8
We know that, CP = SP + Loss = 75 + 8 = Rs 83
Hence, cost price of the bat is Rs 83.
If the price of sugar is decreased by 20%, then the new price of 3kg sugar originally costing Rs 120, will be______.
Original price of 3 kg sugar = Rs 120
Given that, price of sugar is decreased by 20%.
So, new price of sugar = Original price – 20% of original price
= 120 – 20% of 120
= 120- x 120= 120-24=Rs 96 100
Mohini bought a cow for Rs 9000 and Sold it at a loss of Rs 900. The selling price of the cow is_______.
Given, CP of cow=Rs 9000 and loss = Rs 900
We know that, SP = CP – Loss = 9000 – 900=Rs 8100
Hence, the selling price of the cow is Rs 8100.
Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of______% in the transaction.
Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her____ % is___%.
Nasim bought a pen for Rs 60 and sold it for Rs 54. His_____________ % is
Aahuti purchased a house for Rs 5059700 and spent Rs 40300 on its repairing. To make a profit of 5%, she should sell the house for Rs_______ .
If 20 lemons are bought for Rs 10 and sold at 5 for three rupees, then______in the transaction is_____%.
Narain bought 120 oranges at Rs 4 each. He sold 60% of the oranges at Rs 5 each and the remaining at Rs 3.50 each. His_____is_____%.
A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of the apples were found to be rotten. If he sells the remaining apples at Rs 60 per kg, then his_____is_____% .
Interest on Rs 3000 at 10% per annum for a period of 3 yr is______ .
Amount obtained by depositing Rs 20000 at 8% per annum for six months, is_____.
Interest on Rs 12500 at 18% per annum for a period of 2 yr and 4 months is______.
25 mL is_____% of 5 L.
If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then,_____% of A is equal to C.
Interest = , where T is_____,R% is____ and P is____.
Here, T is time period, R% is rate of interest and P is Principal.
The difference of interests for 2 yr and 3 yr on a sum of Rs 2100 at 8% per annum is_______.
To convert a fraction into a per cent, we______ it by 100.
To convert a fraction into a per cent, we multiply it by 100.
To convert a decimal into a per cent, we shift the decimal point two places to the_____.
To convert a decimal into a per cent, we shift the decimal point into places to the right.
The_____of interests on a sum of Rs 2000 at the rate of 6% per annum for yr and 2 yr is Rs 420.
When converted into percentage, the value of 6.5 is______than 100%.
We have, 6.5
In percentage, 6.5 x 100% = 650%
Hence, when converted into percentage, the value of 6.5 is more than 100%.
In questions 68 and 59, copy each number line. Fill in the blanks, so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.
In questions 60 to 79, state whether the statements are True or False.
When an improper fraction is converted into percentage, then the answer can also be less than 100.
Consider, an improper fraction = (N > D)
In percentage, x 100% = 240%
Hence, when an improper fraction is converted into percentage, then the answer is always greater than 100.
8 h is 50% of 4 days.
Let 8 h be x% of 4 days.
The interest on Rs 350 at 5% per annum for 73 days is Rs 35.
The simple interest on a sum of Rs P for T yr at R% per annum is given by the formula
We can also write it as,SI = [since, multiplication is commutative]
75% = 4/3
12% of 120 is 100.
If Ankita obtains 336 marks out of 600, then percentage of marks obtained by her is 33.6%.
Marks obtained by Ankita out of 600 = 336
Percentage, marks = x 100% = 56%
Hence, Ankita got 56% marks.
0.018 is equivalent to 8%.
Given, decimal = 0.018
In percentage, 0.018 x 100= 1.8%
Hence, 0.018 is equivalent to 1.8%
50% of Rs 50 is Rs 25.
Since, 50% of Rs 50 = x 50= Rs 25
Hence, 50% of Rs 50 is Rs 25.
250 cm is 4% of 1 km.
Out of 600 students of a school, 126 go for a picnic. The percentage of students that did not go for the picnic, is 75.
Total students =600 Students went for picnic = 126
∴ Students did not go for picnic = 600 -126= 474
In percentage, x 100% = 79%
Hence, 79% of students did not go for picnic.
By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost price of the book is Rs 60.
If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price of the chair is Rs 2010.
If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of profit is 10%.
Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of 10%, she should have sold the watch for Rs 3300.
Interest on Rs 1200 for yr at the rate of 15% per annum is Rs 180.
Amount received after depositing Rs 800 a period of 3 yr at the rate of 12% per annum is Rs 896.
Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 3 and 5 yr, respectively. The difference in the interests paid by them is Rs 150.
A vendor purchased 720 lemons at Rs 120 per hundred. 10% of the lemons were found rotten, which he sold at Rs 50 per hundred. If he sells the remaining lemons at Rs 125 per hundred, then his profit will be 16%.
Find the value of x, if
(a) 8% of Rs x is ? 100.
(b) 32% of x kg is 400 kg.
(c) 35% of Rs x is ?280.
(d) 45% of marks x is 405.
Imagine that, a 10 x 10 grid has value 300 and that this value is divided evenly among the small squares. In other words, each small square is worth 3. Use a new grid for each part of this problem and label each grid “Value : 300”.
(a) Shade 25% of the grid. What is 25% of 300? Compare the two answers.
(b) What is the value of 25 squares?
(c) Shade 17% of the grid. What is 17% of 300? Compare the two answers.
(d) What is the value of 1/10 of the grid?
Express as a per cent.
Express as a per cent.
In percentage, x 100%=%
Express as a per cent.
In percentage, x 100%= 1%
Express 80% as a fraction in its lowest form.
Express 33 % as a ratio in the lowest form.
Express 16 % as a ratio in the lowest form.
Express 150% as a ratio in the lowest form.
Sachin and Sanjana are calculating 23% of 800.
Now, calculate 52% of 700 using both the ways described above. Which way do you find easier?
Write 0.089 as a per cent.
We have, 0.089
In percentage, 0.089 x 100% = 8.9% [to convert in per cent, multiply by 100]
Write 1.56 as a per cent.
We have, 1.56
In percentage, 1.56 x 100%= 156%
What is 15% of 20?
We have, 15% of 20
= x 20 = 3
What is 800% of 800?
We have, 800% of 800
= x 800 = 6400
What is 100% of 500?
We have, 100% of 500
= x 500= 500
What per cent of 1 h is 30 min?
What per cent of 1 day is 1 min?
What per cent of 1 km is 1000 m?
Find out 8% of 25 kg.
What per cent of Rs 80 is Rs 100?
45% of the population of a town are men and 40% are women. What is the percentage of children?
Percentage of men in town = 45%
Percentage of women in town = 40%
So, percentage of children in town = 100 – 45 – 40= 100 – 85= 15%
Hence, 15% of the population of a town are children.
The strength of a school is 2000. If 40% of the students are girls, then how many boys are there in the school?
As per the given information in the question,
The strength of school = 2000 Percentage of girls in school = 40%
Percentage of boys in school = 100- 40 = 60%
Number of boys in school = 60% of 2000 = x 2000= 60 x 20 = 1200
Hence, number of boys in school is 1200.
Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in kg of chalk.
Percentage of calcium in chalk = 10%
Percentage of carbon in chalk = 3%
Percentage of oxygen in chalk = 12%
800 kg of mortar consists of 55% sand, 33% cement and rest lime. What is the mass of lime in mortar?
Percentage of sand in mortar = 55%
Percentage of cement in mortar = 33%
So, percentage of lime in mortar = 100 – 55 – 33 = 100 – 88 = 12%
∴ Weight of mortar = 800 kg
∴ Mass of lime in mortar = 12% of 800 kg = x 800 = 12 x 8 = 96 kg
Hence, weight of lime in mortar is 96 kg.
In a furniture shop, 24 tables were bought at the rate of Rs 450 per table. The shopkeeper sold 16 of them at the rate of Rs 600 per table and the remaining at the rate of 400 per table. Find her gain or loss per cent.
Medha deposited 20% of her money in a bank. After spending 20% of the remainder, she has Rs 4800 left with her. How much did she originally have?
The cost of a flower vase got increased by 12%. If the current cost is Rs 896, what was its original cost?
Radhika borrowed Rs 12000 from her friends. Out of which Rs 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 yr?
A man travelled 60 km by car and 240 km by train. Find what per cent of total journey did he travel by car and what per cent by train?
Distance covered by car = 60 km
Distance covered by train = 240 km
∴ Total journey = 60 + 240= 300 km
By selling a chair for Rs 1440, a shopkeeper loses 10%. At what price, did he buy it?
Dhruvika invested money for a period from May 2006 to April 2008 at the rate of 12% per annum. If interest received by her is Rs 1620, then find the money invested.
A person wanted to sell a scooter at a loss of 25%. But at the last moment, he changed his mind and sold the scooter at a loss of 20%. If the difference in the two SP’s is Rs 4000, then find the CP of the scooter.
The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women. Find the ratio of the number of literate women to the total population.
In an entertainment programme, 250 tickets of Rs 400 and 500 tickets of Rs 100 were sold. If the entertainment tax is 40% on ticket of Rs 400 and 20% on ticket of Rs 100, then find how much entertainment tax was collected from the programme?
It is given that, 250 tickets of Rs 400 were sold, Therefore, total amount received by selling these tickets = 250 x 400= Rs 100000
Similarly, amount received by selling 500 tickets of Rs 100 = 500 x 100= Rs 50000
It is also given that, 40% and 20% of entertainment tax is on Rs 400 and Rs 100 tickets, respectively.
So, total entertainment tax collected
Bhavya earns Rs 50000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she lias to spent 20% more. Find her new savings.
In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first paper and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70% marks?
A doctor reports blood pressure in millimetres of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.
Manohar is a healthy 37 yr old man whose blood pressure is in the normal category.
(a) Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
(b) If Manohar’s systolic blood pressure is 102 mm Hg, then use the ratio from part (a) to predict his diastolic blood pressure.
(c) Calculate ratio of average systolic to average diastolic blood pressures in the prehypertension category.
(a) Science Application
The king cobra can reach a Length of 558 cm. This is only about 60% of the length of the largest reticulated python. Find the length of the largest reticulated python.
(b) Physical Science Application
Unequal masses will not balance on a fulcrum, if they are at equal distance from it, one side will go up and the other side will go down.
Unequal masses will balance when the following proportion is true.
The child on the left and child on the right are balanced. What is the mass of the child on the right?
(c) Life Science Application
A DNA model was built using the scale 2 cm : 0.0000001 mm. If the model of the DNA chain is 17 cm long, what is the length of the actual chain?
Given below are few mathematical terms.
(a) The ratio of consonants to vowels in each of the terms.
(b) The percentage of consonants in each of the terms.
What’s the Error? An analysis showed that 0.06% of the T-shirts made by one company were defective. A student says this is 6 out of every 100. What is the student’s error?
What’s the Error? A student said that the ratios and were proportional. What error did the student make?
Hence, the ratios are not proportional. To make a ratio proportional to another ratio, we just simply multiply both numerator and denominator by same number.
In our given case, student had multiply numerator by 3 and denominator by 4, which is incorrect.
What’s the Error? A clothing store charges Rs 1024 for 4 T-shirts. A student says that the unit price is Rs 25.6 per T-shirt. What is the error? What is the correct unit price?
A tea merchant blends two varieties of tea in the ratio of 5:4. The cost of first variety is Rs 200 per kg and that of second variety is Rs 300 per kg. If he sells the blended tea at the rate of Rs 275 per kg, then find out the percentage of his profit or loss.
Given, ratio of blended two varieties of tea (green tea : lemon tea) = 5:4
Cost of green tea = Rs 200 per kg
Cost of lemon tea = Rs 300 per kg
SP of blended tea = Rs 275 per kg
According to the ratio,
Let green tea be 5x kg and lemon tea be 4x kg.
Then, cost of green tea = 5x x 200 = Rs 1000x
Cost of lemon tea = 4x x 300 = Rs 1200x
Total CP = 1000x + 1200x = Rs 2200x
Total quantity = 4x + 5x = 9x kg So,
A piece of cloth 5 m long shrinks 10% on washing. How long will the cloth be after washing?
Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?
A memorial trust donates Rs 500000 to a school, the interest on which is to be used for awarding 3 scholarships to students obtaining first three positions in the school examination every year. If the donation earns an interest of 12% per annum and the values of the second and third scholarships are Rs 20000 and Rs 15000 respectively, then find out the value of the first scholarship.
Ambika got 99% marks in Mathematics, 76% marks in Hindi, 61% in English, 84% in Science and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.
What sum of money lent out at 16% per annum simple interest, so that it would produce Rs 9600 as interest in 2 yr?
Harish bought a gas-chullah for Rs 900 and later sold it to Archana at a profit of 5%. Archana used it for a period of two years and later sold it to Babita at a loss of 20%. For how much did Babita get it?
It is given that, Harish bought the chullah for Rs 900 and sold it to Archana at a profit of 5%.
Match each of the entries in Column I with the appropriate entries in Column II
In a debate competition, the judges decide that 20% of the total marks would be given for accent and presentation. 60% of the rest are reserved for the subject matter and the rest are for rebuttal. If this means 8 marks for rebuttal, then find the total marks.
Divide Rs 10000 in two parts, so that the simple interest on the first part for 4 yr at 12% per annum may be equal to the simple interest on the second part for 4.5 yr at 16% per annum.
Given, money= Rs 10000
Now, we have divide Rs 10000 in two parts such that SI on first part for 4 yr at 12%
per annum may be equal to the SI on second part for 4.5 yr at 16%.
Let first part = 7 x
Then, second part = Rs (10000 – x)
Rs 9000 becomes Rs 18000 at simple interest in 8 yr. Find the rate per cent per annum.
In how many years, will the simple interest on a certain sum be 4.05 times the principal at 13.5% per annum?
The simple interest on a certain sum for 8 yr at 12% per annum is Rs 3120 more than the simple interest on the same sum for 5 yr at 14% per annum. Find the sum.
The simple interest on a certain sum for 2.5 yr at 12% per annum is Rs 300 less than the simple interest on the same sum for 4.5 yr at 8% per annum. Find the sum.
Designing a Healthy Diet
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines.
- Calculate your ideal weight as per your height from the table given at the end of this question.
- An active child should eat around 55.11 calories for each kilogram desired weight.
- 55% of calories should come from carbohydrates. There are 4 calories in each gram of carbohydrates.
- 15% of your calories should come from proteins. There are 4 calories in each gram of proteins.
- 30% of your calories may come from fats. There are 9 calories in each gram of fats.
Following is an example to design your own healthy diet.
150 students are studying English, Maths or both. 62% of students study English and 68% are studying Maths. How many students are studying both?
The table lists the world’s 10 largest deserts.
(a) What are the mean, median and mode of the areas listed?
(b) How many times the size of the Gobi Desert is the Namib Desert?
(c) What percentage of the deserts listed are in Asia?
(d) What percentage of the total area of the deserts listed is in Asia?
Earth’s total land is about 148428950 km2. The land area of Asia is about 30% of this total. What is the approximate land area of Asia to the nearest square kilometre?
The pieces of Tangrams have been rearranged to make the given shape.
By observing the given shape, answer the following questions.
(a) What percentage of total has been coloured?
(i) Red (R) =_______
(ii) Blue (B) =_______
(iii) Green (G) =_______
(b) Check that the sum of all the percentages calculated above should be 100.
(c) If we rearrange the same pieces to form some other shape, will the percentage of colours change?
All Subject NCERT Exemplar Problems Solutions For Class 7
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