Maharashtra Board Class 7 Math Solution Chapter 9 – Direct Proportion and Inverse Proportion
Balbharati Maharashtra Board Class 7 Math Solution Chapter 9: Direct Proportion and Inverse Proportion. Marathi or English Medium Students of Class 7 get here Direct Proportion and Inverse Proportion full Exercise Solution.
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Std |
Maharashtra Class 7 |
| Subject |
Math Solution |
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Chapter |
Direct Proportion and Inverse Proportion |
Practice Set 37
1.) If 7 kg onions cost 140 rupees, how much must we pay for 12 kg onions?
ANS:
Here given that 7 kg onions cost 140 rupees.
Then we have to find cost of 12 kg onions.
This is example of direct proportion.
7 kg onions = 140 rupees
12 kg onions =?
By cross multiplication,
? = 140 x 12 / 7
? = 20 x 12
? = 240
The cost of 12 kg onions is 240 rupees.
2.) If 600 rupees buy 15 bunches of feed, how many will 1280 rupees buy?
ANS:
Here given that in 600 rupees buy 15 bunches of feed.
Then we have to find in 1280 rupees how many bunches of feed we buy?
This is example of direct proportion.
15 bunches of feed = 600 rupees
? = 1280 rupees
By cross multiplication,
? = 1280 x 15 / 600
? = 1280 / 40
? = 32
In 1280 rupees we buy 32 bunches of feed.
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?
ANS:
Here given that,
9 cows, 13 kg 500 g of food supplement are required every day
Then we have to find for 12 cows how much food supplement are required every day.
This is example of direct proportion.
9 cows = 13 kg 500 g
12 cows = ?
By cross multiplication,
? = 13 kg 500 g x 12 / 9
? = 13 kg 500 g x 4 / 3
? = 4 kg 500 g x 4
? = 18 kg.
For 12 cows 18 kg food supplement are required every day.
4.) The cost of 12 quintals of soyabean is 36,000 rupees. How much will 8 quintals cost?
ANS:
Here given that,
The cost of 12 quintals of soyabean is 36,000 rupees.
Then we have to find 8 quintals cost.
This is example of direct proportion.
12 quintals = 36,000 rupees
8 quintals =?
By cross multiplication,
? = 36,000x 8 / 12
? =36,000 x 2 / 3
? = 12,000 x 2
? = 24,000
The cost of 8 quintals soyabean is 24,000 rupees.
5.) Two mobiles cost 16,000 rupees. How much money will be required to buy 13 such mobiles?
ANS:
Here given that,
Two mobiles cost 16,000 rupees
Then we have to find cost of 13 mobile phones.
This is example of direct proportion.
2 mobile phones = 16,000 rupees
13 mobile phones =?
By cross multiplication,
? = 16,000x 13 / 2
? =8,000 x 13
? = 1, 04,000
Cost of 13 mobile phones is 1, 04,000 rupees.
Practice Set 38
1.) Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?
ANS:
Here given that,
Five workers take 12 days to weed a field.
Then we have to find 6 workers take how many days and also we have to find 15 workers take how many days?
This is example of inverse proportion.
Five workers take 12 days to weed a field.
Total time = 5 x 12 = 60
Now,
For 6 workers,
We are dividing total time by 6.
60 / 6
= 10 days.
For 6 workers 10 days to weed a field.
For 15 workers,
We are dividing total time by 15.
60 / 15
= 4 days.
For 15 workers 4 days to weed a field.
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?
ANS:
Here given that,
Mohanrao took 10 days to finish a book, reading 40 pages every day.
Then we have to find many pages must he read in a day to finish it in 8 days.
This is example of inverse proportion.
Total work of mohanrao = 10 x 40 = 400
Now, we have to finish the work in 8 days.
We are dividing total work by 8.
400 / 8
= 50 pages.
Mohanrao read 50 pages every day to finish it in 8 days.
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?
ANS:
Here given that, Mary cycles at 6 km per hour.
We have to find for 12 km how much time she take?
For 12 km,
We are dividing 12 km by speed of cycle which is 6 km per hour.
12 / 6
= 2 hours.
Mary takes 2 hours to reach her Aunt’s house which is 12 km.
Total distance = 12 km.
She cycles at a speed of 4 km/hr
We are dividing 12 km by speed of cycle which is 4 km per hour.
12 / 4
= 3 hours.
She cycles at a speed of 4 km/hr she take 3 hours.
4.) The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?
ANS:
Here given that,
The stock of grain in a government warehouse lasts 30 days for 4000 people.
Then we have to find how many days it will last for 6000 people.
This is example of inverse proportion.
Total stock of grain = 30 x 4000
We have to find for 6000 peoples.
We are dividing Total stock of grain by 6000 peoples.
30 x 4000 / 6000
= 1 x 4000 / 200
= 20 days.
For 6000 people stock of grain in a government warehouse lasts 20 days.
Practice Set 39
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?
ANS:
Here given that,
Suresh and Ramesh together invested 144000 rupees in the ratio 4:5 and bought a plot of land.
Total ratio is 9.
Total amount is 1, 44,000 rupees
To find 1 ratio we are dividing 1, 44,000 rupees by 9.
1, 44,000 / 9
1 ratio is 16,000
Suresh invested 4 ratio = 16,000 x 4 = 64,000 rupees.
Ramesh invested 5 ratio =16,000 x 5 = 80,000 rupees.
After some years they sold it at a profit of 20%.
20% = 20 / 100
Profit of Suresh = 64,000 x 20 / 100
Profit of Suresh = 640 x 20
Profit of Suresh = Rs.12, 800
Profit of Ramesh = 80,000 x 20 / 100
Profit of Ramesh = 800 x 20
Profit of Ramesh = Rs.16, 000
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?
ANS:
Here given that,
Viratinvested 50,000.
Samratinvested1, 20,000 rupees.
They suffered a loss of 20%. = 20 / 100
Virat losses = 50,000 x 20 / 100
Virat losses = 500 x 20
Virat losses = Rs. 10,000
Samrat losses = 1, 20,000 x 20 / 100
Samrat losses = 1200 x 20
Samrat losses = Rs.24000
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?
ANS:
Given that,
Shweta, Piyush and Nachiket together invested 80000 rupees.
Shweta’s share of the capital was 30000 rupees.
Piyush’s share of the capital was 12000 rupees.
We have to find Nachiket’s investment =?
Nachiket’s investment =we are subtracting investment of Shweta and Piyush from Rs.80, 000
Nachiket’s investment = 80,000 – (30,000 + 12,000)
Nachiket’s investment =80,000 – 42,000
Nachiket’s investment = Rs.38, 000
At the end of the year they had made a profit of 24%.
Nachiket’s profit = 38,000 x 24 / 100
Nachiket’s profit = 380 x 24
Nachiket’s profit = Rs.9120
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?
ANS:
Given that,
A and B shared a profit of 24500 rupees in the proportion 3:7.
Total profit in the ratio of 3:7.
Total 10 ratio and amount is 24500 rupees
We are finding 1 ratio = 24,500 / 10
Value of 1 ratio = Rs.2450
A profit = 2450 x 3
A profit = Rs.7350
B profit = 2450 x 7
B profit = Rs.17, 150
Each of them gave 2% of his share of the profit to the Soldiers’ Welfare Fund.
A share amount = 7350 x 2 / 100
A share amount = Rs. 147
B share amount = 17150 x 2 / 100
A share amount = Rs.343
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?
ANS:
Given that,
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.
There are total 20 ratio of total 3, 60,000 rupees
We find value of 1 ratio = 3, 60,000 rupees / 20
Value of 1 ratio = 18,000
Jaya have 3 ratio = 3 x 18,000 = Rs. 54,000
Seema have 4 ratio = 4 x 18,000 = Rs. 72,000
Nikhil have 7 ratio = 7 x 18,000 = Rs. 1, 26,000
Neelesh have 6 ratio = 6 x 18,000 = Rs. 1, 08,000
Jaya invested Rs. 54,000.
They made a profit of 12%.
We have to find profit of Nikhil.
Profit of Nikhil = Rs. 1, 26,000 x 12 / 100
Profit of Nikhil = Rs. 1,260 x 12
Profit of Nikhil = Rs.15, 120
