Chain Rule - MCQ 1


20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations | Chain Rule - MCQ 1


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QUESTION: 1

A contractor undertakes to do a job in 18 days. He employees certain number of men, but 12 of them being absent from the very first day, the rest can complete the work in 30 days. The number of men originally employed?

Solution:

Answer – c) 30 Explanation : Let ‘m’ men are originally employed m*18 = (m -12)*30 m = 30

QUESTION: 2

 A contractor employed 60 men to do a piece of work in 76 days. After 50 days, he employed 10 more men and the work was finished 2 day earlier. How many days he would have been behind, if he had not employed additional men?

Solution:

Answer –b) 2 days Explanation : Total work = 60*50 + 70*24 Now days = D D*60 = 60*50 + 70*24
We get D = 78, so 2 more days

QUESTION: 3

 In a dairy farm, 20 horses eat 40 bags of husk in 40 days. In how many days 10 horses will eat 30 bags of husks?

Solution:

Answer – b) 60 Explanation : Horse*Days = Bags 20*40 = 40 and 10*D = 30 (20*40)/(10*D) = 40/30
We get D = 60 days

QUESTION: 4

28 pipes can empty a tank in 4 days working 8 hours a day. If 84 pipes are used to for 5 hours each day, then the same work will be completed in –

Solution:

Answer – d) 2.(2/15) Explanation : 28*4*8 = 84*5*D
D = 2.2/15 days

QUESTION: 5

If 10 labourers can dig a well 40 m deep in 18 days, working 9 hours a day, how many additional labourers should be engaged to dig a similar well 80 m deep in 6 days, each labourer working 9 hours a day?

Solution:

Answer – c) 50 Explanation : 10*18*9 = 40 ……..(1)
L*9*6 = 40 ……..(2)
Divide both equations We get L = 60, so additional 50 men must be employed

QUESTION: 6

If 12 pumps can raise 4800 tonnes of oil in 10 days, working 8 hours a day, in how many days will 16 pumps raise 6000 tonnes of oil, working 12 hours a day?

Solution:

Answer – c) 6.25 days Explanation : (12*10*8)/(16*D*12) = 4800/6000
D = 25/4 days = 6.25 days

QUESTION: 7

An army camp of 6600 men had provisions for 64 days, when given at the rate of 850 grams per head. At the end of 14 days, a troop arrives and it was found that the provisions will last 34 days more, when given 825 grams per head.What is the strength of new troop?

Solution:

Answer – e) 3400 Explanation : 6600*64*850 = 6600*14*850 + M*34*825
we get M = 10000 so new troops = 10000 – 6600 = 3400

QUESTION: 8

 In a school there is a meal for 60 girls and 100 boys. If 50 boys have taken their meal, how many girls will be catered with the remaining meal?

Solution:

Answer – b) 30 Explananion : 50 boys taken the meal means only 1/2 meal is remaining So, G/60 = 1/2, we get G =30

QUESTION: 9

A job that can be completed by 2 men and 6 women in 10 days will be completed by 4 men and 12 women in how many days?

Solution:

Answer – d) 5 Explanation : 2m + 6w = 1/10, m + 3w = 1/20 D is the days required We have to find 4m + 12w = 1/d, 4*(m +3w) = 1/d 4*1/20 = 1/d We get d = 5

QUESTION: 10

If 10 men can reap 40 hectares of a field in 5 days then how many hectares of field can 30 men reap in 10 days?

Solution:

Answer – c) 240 Explanation : 10*5 = 40…….(1)
30*10 = H…….(2)
Divide both equations to get H We get h = 240

QUESTION: 11

10 machines can wash 20 cars in 6 hours. In how many hours can 15 machines wash 40 cars?

Solution:

A) 8
Explanation: Washing cars is a work, so M1*H1*W2 = M2*H2*W1
10*6*40 = 15*H2*20
Solve, H2 = 8 hrs

QUESTION: 12

 To build a house, 5 men take 60 days working 8 hours each day. In how many days 2 such houses can be built by 8 men working 10 hours each day?

Solution:

D) 60
Explanation: Building 1 house is 1, 2 houses is 2, so M1*D1*H1*W2 = M2*D2*H2*W1
5*60*8*(2) = 8*D2*10*(1)
Solve, D2 = 60

QUESTION: 13

2 men and 4 women can complete a job in 5 days. Also same job can be completed by 3 men and 8 women in 3 days. In how many days, twice the job can be completed by 3 men and 3 women?

Solution:

B) 8
Explanation: 2m + 4w = 5D, so 10m + 20w = 1D 3m + 8w = 3D, so 9m + 24w = 1D So, 10m + 20w = 9m + 24w Solve, 1m = 4w From 1st equation(2m + 4w = 5D), 2*4w + 4w = 5D, or 12 women can do in 5 days, so 1 women in 12*5 = 60 days.
Now 3m+3w = 3*4w + 3w = 15 w 1 women in 60 days, so 15 women in 60/15 = 4 days But we are required to find twice work, so 15 women 1 work in 4 days so twice work in 8 days

QUESTION: 14

A job that can be completed by 2 men and 6 women in 10 days will be completed by 5 men and 15 women in how many days?

Solution:

D) 4
Explanation: 2m + 6w = 10 D Or 2(1m + 3w) = 10D Or 1m + 3w = 20D So 5(1m + 3w) = 20/5 Or 5m + 15w = 4D

QUESTION: 15

There is sufficient food for 40 men for a 15 days picnic. If after 6 days 4 men leave, how many more days can the remaining men intake food?

Solution:

D) 1
Explanation: After 6 days, now food is left for 40 men for (15-6) = 9 days, now same food is eaten by (40-4) = 36 men, let it last for x days, so 40*9 = 36*x Solve, x = 10 The food which was to last for 9 days for 40 men, now will last for 10 days for 36 men, so extra 1 day.

QUESTION: 16

 A job is completed by 5 men or 7 women in 40 days, then in how many days thrice the job as previous will be completed by 5 men and 3 women?

Solution:

D) 84
Explanation: 5 m or 7 w 5m + 3w Cross multiply and put in denominator Days = 40*5*7/ [5*3 +7*5] = 28 so for thrice work, days = 28*3

QUESTION: 17

10 women completed 2/7th of work in 18 days working 6 hours each day. After this 5 women left and 2 men joined. In how many days working same number of hours, the remaining work will get completed if 1 man is equal to 2 women?

Solution:

A) 50
Explanation: Remaining work = 1 – 2/7 = 5/7 After 18 days, 5 women left and 2 men joined so 4 women joined (1m = 2w), now number of women is 5+4 = 9, so 10*18*6*(5/7) = 9*D2*6*(2/7)
Solve, D2 = 50

QUESTION: 18

20 carpets are to weave by 40 women in 50 days working 8 hours per day. After 20 days, order of 6 more carpets came. To complete the total work on time, how many more hours per day they will have to work?

Solution:

B) 4
Explanation: First find the number of carpets weave in first 20 days, after which order of more carpets came. So, In 50 days, 20 carpets, so in 20 days 20*20/50 = 8 carpets So in remaining 30 days, (20-8) = 12 carpets can be weave working 8 hrs each day Now number of carpets is (12+6) = 18, let no of hours is x, so H1*W2 = H2*W1
8*18 = x*12 Solve, x = 12 hrs So more hrs = 12-8 = 4 hrs

QUESTION: 19

 A work is to completed. 10 men started the work and completed 1/6th of the work in 5 days working 3 hrs each day. 2 more men are employed. In how many days will the total number of men complete four times work as before working 5 hours each day?

Solution:

C) 10
Explanation: M2 = (10+2) = 12 men, W2 = 4*(1/6) = 4/6 So 10*5*3*(4/6) = 12*D2*5*(1/6)
Solve, D2 = 10

QUESTION: 20

2 men or 4 women or 5 children can complete a piece of work in 38 days. In how many days will 1 man, 1 woman and 1 child complete the same work?

Solution:

B) 40
Explanation: 2 men or 4 women or 5 children = 38 D So 1m + 1w + 1c = 38*2*4*5/(2*4 + 4*5 + 5*2)

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