Question 1

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be fi…

Accepted Answer

[(100 x 35) + (200 x 5)]men can finish the work in 1 day Therefore, 4500 men can finish the work in 1 day. 100 men can finish it in 4500/100= 45 days. This is 5 days behind Schedule

Question 2

If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?

Accepted Answer

Let the required no of binders be X. Less books , Less binders (Direct Proportion) More days, Less binders (Indirect proportion) B o o k s 900 : 660 D a y s 12 : 10 ⋮ ⋮ 18 : x Therefore, (900 * 12 * x) = (660 * 10 * 18) => x = 11

Question 3

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

Accepted Answer

Less Men, means more Days {Indirect Proportion} Let the number of days be x then, 27 : 36 :: 18 : x [Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)] =>27x = 36 * 18 => x = 24 So 24 days will be required to get work done by 27 men.

Question 4

If a quarter kg of carrots costs 60 paise, how many paise will 200 gms cost ?

Accepted Answer

Quarter of Kg means 250 gm Less weight, less price (Direct Proportion) So, 250 : 200 :: 60 : x => x = 48 So 200 gm will cost 48 paise.

Question 5

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero ?

Accepted Answer

If we consider the third term to be ‘x” The 15th term will be (x + 12d) 6th term will be (x + 3d) 11th term will be (x + 8d) and 13th term will be (x + 10d). Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0. x + 9d will be the 12th term. Thus, 12th term of the A.P will be zero.

Question 6

Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in

Accepted Answer

Let x men can do the in 12 days and the required number of days be z More men, Less days [Indirect Proportion] Less work, Less days [Direct Proportion ] m e n 2 x : x w o r k 1 : 1 2 : : 12 : z ∴ 2 x × 1 × z = x × 1 2 × 12 ⇒ z = 3

Question 7

In a queue, Shankar is ninth from the rear end. Althaf's place is eighth from the front. Nitu is standing between the two. What could be the minimum numbers of boys standing in the queue ?

Accepted Answer

1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14 Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them So minimum no. of boys standing in the queue = 14

Question 8

If a person having Rs. 2000 and he want to distribute this to his five children in the manner that each son having Rs. 30 more than the younger one , what will be the share of youngest child ?

Accepted Answer

Assume first child (the youngest) get = Rs. x According to the question ; each son having Rs. 30 more than the younger one Second child will get = Rs. x + 30 Third child will get = Rs. x + 30 + 30 = x + 60 Forth child will get = Rs. x + 30 + 30 + 30 = x + 90 Fifth child will get = Rs. x + 30 + 30 + 30 + 30 = x + 120 Total amount they got = Rs. 2000 x + (x+30) + (x+60) + (x+90) + (x+120) = 2000 5x + 300 = 2000 5x = 1700 x = Rs. 340 So the youngest child will get Rs. 340.

Question 9

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

Accepted Answer

Let the required no of hectares be x. Then More men, More hectares (Direct proportion) More days, More hectares (Direct proportion) M e n 8 : 36 D a y s 24 : 30 ⋮ ⋮ 80 : x => ( 8 * 24 * x) = (36 * 30 * 80) => x= 450

Question 10

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 × 35 125 = 42

Question 11

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/x).y] = Rs.(yd/x)

Question 12

If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?

Accepted Answer

Let the Required cost be X paise. Less Weight , Less cost (Direct Proportion) Therefore, 250 : 200 :: 60 : x => (250 * x) = (200 * 60) => x= 48

Question 13

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) c o w s 1 : 40 : 40 : x b a g s 40 : 1 : 40 : x 1 x 40 x x = 40 x 1 x 40 => x = 40.

Question 14

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) w e a v e r s 4 : 8 } : 4 : x d a y s 4 : 8 } : 4 : x 4 x 4 x x = 8 x 8 x 4 => x = 8 * 8 * 4 4 * 4 => x = 16.

Question 15

10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?

Accepted Answer

More Men, Less Hours {Indirect Proportion} Less Days, More Hours {Indirect Proportion} m e n 15 : 10 d a y s 12 : 18 ⋮ ⋮ 6 : x => 15 * 12 * x = 10 * 18 * 6 =>x = 6

Question 16

If 16 men working 7 hours day can plough a fieid in 4l days, inhow many days will 14 men working 12 hours a clay plough the samefield ?

Accepted Answer

(Men 14 : 16) : (Hrs/Day 12 : 7) :: 48 : x 14 * 12 * x = 16 * 7 * 48 or x = 32

Question 17

If the Price of 6 toys is Rs. 264.37, What will be the approximate price of 5 toys?

Accepted Answer

Let the required Price be Rs. X .Then, Lest toys , Less cost (Direct Proportion) Therefore 6 : 5 :: 264.37 : x => 6 * x = 5 * 264.37 => X= 220.308 Therefore, Approximate price of 5 toys = Rs. 220

Question 18

An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ?

Accepted Answer

Given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in, 1.14 ----- 1 52.0 ------? ⇒ 52 1 . 14 = 45.61 sec

Question 19

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 = 120 200 50 =30men

Question 20

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

Accepted Answer

Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, 0.128 : 1 :: 25 : x ⇒ x = 1 × 25 0 . 128 => x = 195.31 So time will be approx 195 seconds

Chain Rule Questions