Learn and practice Problems on chain rule with easy explaination and shortcut tricks. All questions and answers on chain rule covered for various Competitive Exams

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1) If 15 men can reap the crops of a field in 28 days, in how many days will 5 men reap it?

Let 5 men can reap a field in x days So, put the same quantities on the same side. Men: Days Now, Men and Days are inversely proportional to each other. If we increase the number of men fewer days will be required to complete the work. Inversely proportional means 15: 1/25 5: 1/x 5/15 =28/x

i.e., 5: 15 = 28: x Or, x = (28*15)/ 5 Or, x = 84 days Hence, 5 men can reap a field in 84 days.

2) If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?

i. If 8 men can reap 80 hectares, then how many hectares can reap by 36 men in the same number of days Now, the same type should be on the same side Let the required number of hectares = x Men and hectares are directly proportional to each other. So, 8: 36 = 80: x Or, x = (36*80)/8 Or, x = 360 hectares

ii. If 360 hectares in 24 days, then how many hectares can reap in 30 days? Similarly, 24: 30 = 360: x So, x = (360*30)/24 Or, x = 450 Hence, 36 men can reap 450 hectares in 30 days.

Solution 2: We know that 8 men work 24 days and reap a field of 80 hectares. Similarly, 36 men work 30 days and reap a field of x (let) hectares. Now, we know that men * days = total work So, 8*24 = 192, that means total work done is equals to 192 Now, 36*30 = 1080, that means the work done by 36 men is 1080 unit. Now, put the same unit on same side Or, 192: 1080 = 80: x Or, x = (1080*80)/ 192 = 450 Hence, 36 men can reap 450 hectares in 30 days.

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3) A fort had arrangements for 150 boys for 45 days. After 10 days, 25 boys left the fort. Then after how much time the food will be consumed completely if the consumption of food remains the same for the remaining boys?

ATQ, 25 people left the fort after 10 days, but still, the remaining food will be consumed at the same rate. That means if the 150 boys continue till the end, then the remaining food would last for 150 boys for (45-10) = 35 days. Now After 10 days the remaining food will be (boys * days) 150 * 35 = 5250 unit But the 25 boys left the for after 10 days i.e., 125 boys will consume the 5250 unit food in x days Now, x = 5250/125 = 42 days. That means the remaining food will last for 42 days.

Solution 2: The remaining food would last for 150 boys for (45-10) = 35 days. But as 25 boys have gone out, the remaining food would last for a long period (x). The number of boys and consumption of food are inversely proportional to each other. That means, 125 boys: 150 boys = 35 days: x Or, x = (150*35)/ 125 = 42 days Hence, 125 boys require 42 days to consume the remaining food.

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4) If 30 men can complete a piece of work in 27 days, in what time 18 men can do another piece of work 3 times as greater?

30 men can do a piece of work in 27 days, and we know that men* days = total work So, we can say that the total work = 30*27 = 810 units Now ATQ, 18 men can do work 3 times greater than 810 units. i.e., 18 men can do a work 3*810 = 2430 units in x days Men *days = total work (2430 units) 18 * x = 2430 x = 2430/18 = 135 days

Solution 2: Let the number of days required to do a work = x Now, 30 men can do a piece of work in 27 days. ATQ, if the work gets 3 times, then 18 men can finish the work in how many days. Now, put the same unit on the same side. i.e., if the work is the same as previous, then 18 men: 30 men = 27 days: x days Or, x = (30*27)/ 18 But ATQ, the work gets 3 times greater So, x = (30*27*3)/ 18 = 2430/18 = 135 days Hence, 18 men can finish the other work which is 3 times greater than previous work in 135 days.

5) If 9 engines consume 24 metric tons of coal, when each is working 8 hours per day, how much coal should be available for 8 engines, each running 13 hours per day, it is given that 3 engines of the former type consume as much as 4 engines of later type.

We have: The lesser engines, less coal consumed More working hours, more coal consumed Both the cases are directly proportional. If three engines of former type consume 1 unit, 1 engine will consume 1/3 unit. If four engines of latter type consume 1 unit, 1 engine will consume ¼ units. And, less rate of consumption, less coal consumed. Now, Number of engines = 9: 8 Working hours = 8:13

Therefore, rate of consumption = 1/3 : 1/4

Let the coal consumed by 8 engines is x metric tones

Hence, the required coal = 26 metric tons.

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6) A contract is to be finished in 46 days and 117 men involved in it, each working 8 hours per day. After 33 days, 4/7 of the work is finished, how many additional men may be employed so that it may be completed in time, each man now working 9 hours a day?

Remaining period = 46-33 = 13 days Now, we have Less work, less man (directly proportion) Less days, more men (inverse proportion) More hours/days, less man (inverse proportion)

Now, we can say that work = 4/7 : 3/7

Therefore, days = 13: 33 And, hours/day = 9: 8

Therefore,

Where, x is total number of men after 33 days.

Therefore, extra men to be employed = 198 – 117 = 81.

7) 24 women or 15 men or 36 boys can finish a piece of work in 12 days, working 8 hours per day, how many men must be associated with 12 women and 6 boys to finish another piece of worktimes as greater in 30 days working 6 hours a day?

We have 15 men = 24 women Or, 12 women = 7.5 men Also, 36 boys = 15 men 6 boys = 15/6 = 5/2 = 2.5 men Therefore, 12 women + 6 boys = 7.5 + 2.5 men= 10 men Now, The number of day’s ratio is 30: 12 The hour’s ratio is 6 hours: 8 hours

The work ratio is 1 work: 2 * 1/4 works

Now, we can say that

Where x is the total number of men

Therefore, the total number of men = 18 So, 18-10 = 8 men must be associated.

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8) The price of 357 mangoes is Rs 1517.25. Find the approximate price of 49 dozens of such mangoes?

We know that 1 dozen = 12 piece 49 dozens =49*12 = 588 mangoes Let x is the price for 588 mangoes. Now, put the same unit on the same side Price and mangoes are directly proportional to each other, so 357 mangoes: 588 mangoes = 1517.25: x Or, x = [1517.25* 588]/ 357 = 2499 Hence, the approximate value, x = Rs. 2500.

9) If 2 kg of almonds cost as much as 8 kg of walnuts, and the cost of 5 kg of almonds and 16 kg of walnuts is Rs 1080, what is the cost of almonds per kg?

Let the cost of almond per kg be Rs x, and the cost of walnuts per kg be Rs y. Now, ATQ, 2x = 8y or x = 4y Now, 5x+ 16y = 1080 Or, 5x+4x = 1080 Or, x = 120 Therefore, the cost price of almond per kg = Rs. 120

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10) If 16 men working 7 hours a day can plow a field in 48 days, in how many days will 14 men working 12 hours a day plow the same field?

Let the one-day work = number of men* total working hours per day Now, the ratio of total work = (14*12): (16*7) Now, the ratio of days = 48: x Where x is the required number of days Now, one day work is inversely proportional to the number of days: So, (14*12): (16*7) = 48: x Or, x = (48*16*7)/ (14*12) = 32 Therefore, 32 days are required to plow the same field.