Question 1

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

Accepted Answer

Let the required number of days be x Less cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) Cows 1 : 40 ] :: 40 : x Bags 40 : 1 ∴ 1 x 40 x x = 40 x 1 x 40 ⟹ x = 40.

Question 2

36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

Accepted Answer

Let the required number of days be x Less men, More days (Indirect Proportion) ∴ 27 : 36 :: 18 : x ⟺ 27 x x = 36 x 18 ⟹ x = 36 x 18 27 ⟹ x = 24.

Question 3

3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Accepted Answer

Let the required number of working hours per day be x More pumps, Less working hours per day (Indirect Proportion) Less days, More working hours per day (Indirect Proportion) Pumps 4 : 3 ] :: 8 : x Days 1 : 2 ∴ 4 x 1 x x = 3 x 2 x 8 ⟹ x = (3 x 2 x 8) (4) ⟹ x = 12.

Question 4

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

Accepted Answer

Let the required number of bottles be x More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) Wavers 4 : 8 ] :: 4 : x Days 4 : 8 ∴ 4 x 4 x x = 8 x 8 x 4 ⟹ x = (8 x 8 x 4) (4 x 4) ⟹ x = 16.

Question 5

A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:

Accepted Answer

Let the height of the building x metres. Less lengthy shadow, Less in the height (Direct Proportion) ∴ 40.25 : 28.75 :: 17.5 : x ⟺ 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 40.25 ⟹ x = 12.5

Question 6

An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?

Accepted Answer

Let the required time be x seconds. More metres, More time (Direct Proportion) ∴ 0.128 : 25 :: 1 : x ⟺ 0.128x = 25 x 1 x = 25 = 25 x 1000 0.128 128 ⟹ x = 195.31. ∴ Required time = 195 sec (approximately).

Question 7

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

Accepted Answer

Let the required number days be x Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) Spiders 1 : 7 ] :: 7 : x Webs 7 : 1 ∴ 1 x 7 x x = 7 x 1 x 7 ⟹ x = 7.

Question 8

In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

Accepted Answer

There is a meal for 200 children. 150 children have taken the meal. Remaining meal is to be catered to 50 children. Now, 200 children ≡ 120 men. 50 children ≡ ❨ 120 x 50 ❩ = 30 men. 200

Question 9

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

Accepted Answer

Let the required number of revolutions made by larger wheel be x Then, More cogs, Less revolutions (Indirect Proportion) ∴ 14 : 6 :: 21 : x ⟺ 14 x x = 6 x 21 ⟹ x = 6 x 21 14 ⟹ x = 9.

Question 10

If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?

Accepted Answer

Cost of x metres = Rs. d. Cost of 1 metre = Rs. ❨ d ❩ x Cost of y metres = Rs. ❨ d . y ❩ = Rs. ❨ yd ❩. x x

Question 11

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Accepted Answer

Let the required number of bottles be x More machines, More bottles (Direct Proportion) More minutes, More bottles (Direct Proportion) Machines 6 : 10 ] :: 270 : x Time (in minutes) 1 : 4 ∴ 6 x 1 x x = 10 x 4 x 270 ⟹ x = (10 x 4 x 270) (6) ⟹ x = 1800.

Question 12

If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

Accepted Answer

Let the required weight be x kg. Less weight, Less cost (Direct Proportion) ∴ 250 : 200 :: 60 : x ⟺ 250 x x = (200 x 60) ⟹ x= (200 x 60) 250 ⟹ x = 48.

Question 13

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

Accepted Answer

After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) ∴ 125 : 150 :: 35 : x ⟺ 125 x x = 150 x 35 ⟹ x = 150 x 35 125 ⟹ x = 42.

Question 14

A man completes 5⁄8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

Accepted Answer

Work done = 5 8 Balance work = ❨ 1 - 5 ❩ = 3 8 8 Let the required number of days be x. Then, 5 : 3 = :: 10 : x ⟺ 5 x x = 3 x 10 8 8 8 8 ⟹ x = ❨ 3 x 10 x 8 ❩ 8 5 ⟹ x = 6.

Question 15

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

Accepted Answer

Let the required number of days be x Less persons, More days (Indirect Proportion) More working hours per day, Less days (Indirect Proportion) Persons 30 : 39 ] :: 12 : x Working hours/day 6 : 5 ∴ 30 x 6 x x = 39 x 5 x 12 ⟹ x = (39 x 5 x 12) (30 x 6) ⟹ x = 13.

Question 16

If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?

Accepted Answer

Let the required length be x meters More men, More length built (Direct proportion) Less days, Less length built (Direct Proportion) M e n 20 : 35 D a y s 6 : 3 ⋮ ⋮ 56 : x => (20 x 6 x X)=(35 x 3 x 56) => x = 49 Hence, the required length is 49 m.

Question 17

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Accepted Answer

Originally let there be x men. Less men, More days (Indirect Proportion) Therefore, (x-10) : x :: 100 :110 => (x - 10) * 110 = x * 100 => x= 110

Question 18

If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?

Accepted Answer

Let the required no of hours be x. Then Less men , More hours (Indirct Proportion) Therefore, 15:36 ::25:x => (15 x X)=(36 x 25) => x = 60 Hence, 15 men can do it in 60 hours.

Question 19

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in

Accepted Answer

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys =>5 men= 10 boys => 1man= 2 boys Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys ( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys. Let the required number of days be x. More boys , Less days (Indirect proportion) More work , More days (Direct proportion) B o y s 22 : 11 W o r k 1 : 3 ⋮ ⋮ 14 : x Therefore, (22 * 1 * x) = (11 * 3 * 14) => x = 21 Hence, the required number of days = 21

Question 20

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

Accepted Answer

Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) S p i d e r s 1 : 7 W e b s 7 : 1 ⋮ ⋮ 7 : x => 1 * 7 * x = 7 * 1 * 7 => x= 7

Chain Rule Questions