Std 7 Mathematics · Chapter 9

9. Direct Proportion and Inverse Proportion

Step-by-step solutions to Practice Sets 37 to 39. Maharashtra State Board (Balbharati), Grade Seven Mathematics, Part Two.

Practice Set 37

In each question the two quantities are in direct proportion — when one increases, the other increases in the same ratio — so their ratio stays constant.

1If 7 kg onions cost 140 rupees, how much must we pay for 12 kg onions?

Let the cost of 12 kg onions be x rupees.

7140 = 12x
∴ 7x = 140 × 12 = 1680
∴ x = 16807 = 240

We must pay ₹ 240.

2If 600 rupees buy 15 bunches of feed, how many will 1280 rupees buy?

Let 1280 rupees buy x bunches.

60015 = 1280x
∴ 600x = 1280 × 15 = 19200
∴ x = 19200600 = 32

1280 rupees will buy 32 bunches of feed.

3For 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?

13 kg 500 g = 13.5 kg. Let x kg be needed for 12 cows.

913.5 = 12x
∴ 9x = 13.5 × 12 = 162
∴ x = 1629 = 18

18 kg of food supplement is needed for 12 cows every day.

4The cost of 12 quintals of soyabean is 36,000 rupees. How much will 8 quintals cost?

Let 8 quintals cost x rupees.

1236000 = 8x
∴ 12x = 36000 × 8 = 288000
∴ x = 28800012 = 24000

8 quintals will cost ₹ 24,000.

5Two mobiles cost 16,000 rupees. How much money will be required to buy 13 such mobiles?

Let 13 mobiles cost x rupees.

216000 = 13x
∴ 2x = 16000 × 13 = 208000
∴ x = 104000

₹ 1,04,000 will be required.

Practice Set 38

In each question the two quantities are in inverse proportion — when one increases, the other decreases — so their product stays constant.

1Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?

Workers × days = 5 × 12 = 60 (constant).

6 workers: 6 × x = 60, ∴ x = 10
15 workers: 15 × x = 60, ∴ x = 4

6 workers would take 10 days and 15 workers would take 4 days.

2Mohanrao 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?

Days × pages per day = 10 × 40 = 400 (total pages in the book).

8 × x = 400
∴ x = 50

He must read 50 pages a day.

3Mary 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?

Speed × time = distance = 12 km (constant).

At 6 km/hr: 6 × x = 12, ∴ x = 2
At 4 km/hr: 4 × x = 12, ∴ x = 3

She will take 2 hours at 6 km/hr and 3 hours at 4 km/hr.

4The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?

People × days = 4000 × 30 = 120000 (constant).

6000 × x = 120000
∴ x = 1200006000 = 20

The stock will last 20 days for 6000 people.

Practice Set 39

In a partnership, profit or loss is shared in the same proportion as the capital invested.

1Suresh 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?

Total profit = 144000 × 20100 = 28800 rupees
Let Suresh’s profit be 4k and Ramesh’s 5k.
4k + 5k = 28800 ∴ 9k = 28800 ∴ k = 3200
Suresh’s profit = 4 × 3200 = 12800
Ramesh’s profit = 5 × 3200 = 16000

Suresh got ₹ 12,800 and Ramesh got ₹ 16,000.

2Virat 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?

Ratio of investments = 50000 : 120000 = 5 : 12
Total capital = 170000; total loss = 170000 × 20100 = 34000 rupees
Let the losses be 5k and 12k. 17k = 34000 ∴ k = 2000
Virat’s loss = 5 × 2000 = 10000
Samrat’s loss = 12 × 2000 = 24000

Virat lost ₹ 10,000 and Samrat lost ₹ 24,000.

Check: each lost 20% of what he invested — 20% of 50000 = 10000, 20% of 120000 = 24000.

3Shweta, 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 investment = 80000 − (30000 + 12000) = 38000 rupees
Total profit = 80000 × 24100 = 19200 rupees
Ratio of investments = 30000 : 12000 : 38000 = 15 : 6 : 19
15k + 6k + 19k = 19200 ∴ 40k = 19200 ∴ k = 480
Nachiket’s profit = 19 × 480 = 9120

Nachiket invested ₹ 38,000 and his share of the profit was ₹ 9,120.

4A 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?

3k + 7k = 24500 ∴ 10k = 24500 ∴ k = 2450
A’s share = 3 × 2450 = 7350; B’s share = 7 × 2450 = 17150
A gave 7350 × 2100 = 147 rupees
B gave 17150 × 2100 = 343 rupees

A gave ₹ 147 and B gave ₹ 343 to the Fund.

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?

3k + 4k + 7k + 6k = 360000 ∴ 20k = 360000 ∴ k = 18000
Jaya’s capital = 3 × 18000 = 54000 rupees
Total profit = 360000 × 12100 = 43200 rupees
Profit per part = 4320020 = 2160
Nikhil’s profit = 7 × 2160 = 15120

Jaya’s share in the capital was ₹ 54,000 and Nikhil’s profit was ₹ 15,120.

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