Mathematics Solutions Solutions for Class 7 Maths Chapter 10 Direct Proportion And Inverse Proportion are provided here with simple step-by-step explanations. These solutions for Direct Proportion And Inverse Proportion are extremely popular among Class 7 students for Maths Direct Proportion And Inverse Proportion Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 7 Maths Chapter 10 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 7 Maths are prepared by experts and are 100% accurate.

#### Question 1:

If 7 kg onions cost 140 rupees, how much must we pay for 12 kg onions?

Let us suppose the cost of 12 kg onions is x rupees.
The number of onions and their cost vary in direct proportion.
$\therefore \frac{7}{140}=\frac{12}{x}\phantom{\rule{0ex}{0ex}}⇒x=\frac{12×140}{7}$
= 240 rupees
Hence, the cost of 12 kg onions is 240 rupees.

#### Question 2:

If 600 rupees buy 15 bunches of feed, how many will 1280 rupees buy?

Let us suppose x bunches of feed can be bought in 1280 rupees.
The number of bunches of feed and their cost vary in direct proportion.
$\therefore \frac{15}{600}=\frac{x}{1280}\phantom{\rule{0ex}{0ex}}⇒x=\frac{15×1280}{600}$
= 32
Hence, 32 bunches of feed can be bought in 1280 rupees.

#### Question 3:

For 9 cows, 13 kg 500 g of food supplement are required every day. In the same proportion, how much will be needed for 12 cows?

Let us suppose x kg of food supplement required for 12 cows.
The quantity of food supplement and the number of cows vary in direct proportion.
$\therefore \frac{9}{13.5}=\frac{12}{x}\phantom{\rule{0ex}{0ex}}⇒x=\frac{12×13.5}{9}$
= 18 kg
Hence, 18 kg of food supplement required for 12 cows.

#### Question 4:

The cost of 12 quintals of soyabean is 36,000 rupees. How much will 8 quintals cost?

Let us suppose the cost of 8 quintals of soyabean is x rupees.
The quantity of soyabeans and their cost vary in direct proportion.
$\therefore \frac{12}{3600}=\frac{8}{x}\phantom{\rule{0ex}{0ex}}⇒x=\frac{8×3600}{12}$
= 24000 rupees
Hence, the cost of 8 quintals of soyabean is 24000 rupees.

#### Question 5:

Two mobiles cost 16,000 rupees. How much money will be required to buy 13 such mobiles ?

Let us suppose the cost of 13 mobiles is x rupees.
The number of mobiles and their cost vary in direct proportion.
$\therefore \frac{2}{16000}=\frac{13}{x}\phantom{\rule{0ex}{0ex}}⇒x=\frac{13×16000}{2}$
= 104000 rupees
Hence, the cost of 13 mobiles is 104000 rupees.

#### Question 1:

Five workers take 12 days to weed a field. How many days would 6 workers take ? How many would 15 take ?

Let us suppose 6 workers will take x days to weed a field.
As the number of workers increases, the number of days decreases.
So, the number of workers and number of days are in inverse proportion.
∴ 5 × 12 = 6 × x
$⇒x=\frac{60}{6}$
⇒ x = 10 days
Let us suppose 15 workers will take y days to weed a field.
∴ 5 × 12 = 15 × y
$⇒y=\frac{60}{15}$
⇒ y = 4 days
Hence, 6 workers will take 10 days, while 15 workers will take 4 days to weed a field.

#### Question 2:

Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days?

Let us suppose Mohanrao will have to read x pages every day to finish the book in 8 days.
As the number of days decreases, the number of pages increases.
So, the number of days and number of pages are in inverse proportion.
∴ 10 × 40 = 8 × x
$⇒x=\frac{400}{8}$
⇒ x = 50 pages
Hence, Mohanrao will have to read 50 pages every day to finish the book in 8 days

#### Question 3:

Mary cycles at 6 km per hour. How long will she take to reach her Aunt’s house which is 12 km away ? If she cycles at a speed of 4 km/hr, how long would she take ?

Given:
Case -1:
Speed = 6 km/hr
Distance = 12 km
$\therefore \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}\phantom{\rule{0ex}{0ex}}=\frac{12}{6}$
= 2 hours
Case -2:
​Speed = 4 km/hr
Distance = 12 km
$\therefore \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}\phantom{\rule{0ex}{0ex}}=\frac{12}{4}$
= 3 hours
Hence, if the speed of cycle is 6 km/hr then, Marry will take 2 hours and if the speed of cycle is 4 km/hr then, she will take 3 hours to reach her Aunt’s house.

#### Question 4:

The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people ?

Let us suppose the stock of grain in a government warehouse lasts x days for 6000 people.
As the number of people increases, the number of days decreases.
So, the number of days and number of people are in inverse proportion.
∴ 30 × 4000 = 6000 × x
$⇒x=\frac{120000}{6000}$
⇒ x = 20 days
Hence, the stock of grain in a government warehouse lasts 20 days for 6000 people.

#### Question 1:

Suresh and Ramesh together invested 144000 rupees in the ratio 4:5 and bought a plot of land. After some years they sold it at a profit of 20%. What is the profit each of them got?

The proportion of Suresh's and Ramesh’s investment is 4:5.
The profit is shared in the same proportion as the investment, hence, proportion of profit is 4:5.
Now, profit = $\frac{20}{100}×144000$
= 28800 rupees
Therefore, the profit of Suresh and Ramesh  is given by
Suresh's profit = $\frac{4}{9}×28800$
= 12800 rupees
Ramesh's profit = $\frac{5}{9}×28800$
= 16000 rupees
Hence, Suresh and Ramesh got the profit of 12800 and 16000 rupees respectively.

#### Question 2:

Virat and Samrat together invested 50000 and 120000 rupees to start a business. They suffered a loss of 20%. How much loss did each of them incur ?

The proportion of Virat's and Samrat’s investment is given by
50000:120000 = 5:12
The loss is shared in the same proportion as the investment, hence, proportion of profit is 5:12.
Now, Loss = $\frac{20}{100}×\left(50000+120000\right)$
$\frac{20}{100}×\left(170000\right)$
= 34000 rupees
Therefore, the loss incurred by Virat and Samrat is given by
Virat's loss = $\frac{5}{17}×34000$
= 10000 rupees
Samrat's loss = $\frac{12}{17}×34000$
= 24000 rupees
Hence, Virat and Samrat incurred the loss of ​10000 and 24000 rupees respectively.

#### Question 3:

Shweta, Piyush and Nachiket together invested 80000 rupees and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was 30000 rupees and Piyush’s 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit?

Nachiket’s investement = Total investment − (Shweta’s investment + Piyush’s investment)
= 80000 − (30000 + 12000)
= 80000 − 42000
= 38000 rupees
The proportion of Shweta's, Piyush's and Nachiket's investment is given by
30000:12000:38000 = 15:6:19
The profit is shared in the same proportion as the investment, hence, proportion of profit is 15:6:19.
Now, Profit = $\frac{24}{100}×\left(80000\right)$
= 19200 rupees
Therefore, Nachiket’s share of the profit is given by
$\frac{19}{40}×19200$
= 9120 rupees
Hence, Nachiket’s investment and his share of the profit are ​38000 and 9120 rupees respectively.

#### Question 4:

A and B shared a profit of 24500 rupees in the proportion 3:7. Each of them gave 2% of his share of the profit to the Soldiers’ Welfare Fund. What was the actual amount given to the Fund by each of them?

Amount of share to the Soldiers’ Welfare Fund = 2% of 24500
= 490 rupees
The profit is shared in the proportion 3:7.
Therefore, A’s share to the Fund is given by
$\frac{3}{10}×490$
= 147 rupees
Therefore, B’s share to the Fund is given by
= ​$\frac{7}{10}×490$
= 343 rupees
Hence, A's and B's share to the fund are 147 and 343 rupees respectively.

#### Question 5:

Jaya, Seema, Nikhil and Neelesh put in altogether 360000 rupees to form a partnership, with their investments being in the proportion 3 : 4 : 7 : 6. What was Jaya’s actual share in the capital ? They made a profit of 12%. How much profit did Nikhil make ?

Total investment = 360000 rupees
Total profit = $\frac{12}{100}×360000$
= 43200 rupees
The profit is shared in the same proportion as the investment, hence, proportion of profit is 3:4:7:6.
Jaya's share is given by
$\frac{3}{20}×360000$
= 54000 rupees
Nikhil's share in the profit is given by
$\frac{7}{20}×43200$
= 15120 rupees
Hence, Jaya's share and Nikhil's profit are 54000 and 15120 rupees respectively.

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