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 Application sums
1) A is 20 % more efficient than B to complete the work. Both of them together complete the work in 5 5/11 days. Find the number of days taken by A alone to complete the work?
a) 10 days
b) 16 days
c) 12 days
d) 14 days
e) None of these
2) 35 men can complete a piece of work in 18 days. After 8 days from the start of the work, some men left. If the remaining work was completed by the remaining men in 14 days, then find the men left after 8 days from the start of the work?
a) 10 men
b) 12 men
c) 8 men
d) 14 men
e) None of these
3) A contractor hired 40 men to complete a project in 15 days. 40 men started working, after 9 days the contractor notices that only three-fifth of the work gets completed. Then how many extra men can be employed to complete the remaining work on time?
a) 0
b) 5
c) 10
d) 8
e) None of these
4) P and Q can complete the work alone in x days and (x + 10) days respectively. They work together to complete the work in 6 2/3 days. Find the efficiency ratio of P to that of Q?
a) 4 : 3
b) 2 : 1
c) 5 : 4
d) 6 : 5
e) None of these
5) 12 men can complete a work in 15 days and 15 women can complete the same work in 24 days. Then find 15 men and 20 women can complete the work?
a) 8 2/3 days
b) 9 5/6 days
c) 10 ¾ days
d) 7 1/5 days
e) None of these
6) 46 women earned Rs. 172500 by working 25 days. How many men must work for 24 days to receive Rs. 230400 provided the daily wages of a man is twice that of a woman?
a) 30 men
b) 32 men
c) 28 men
d) 34 men
e) None of these
7) A father is 2 times faster than his son. If the son can complete a piece of work in 16 days, then how long will it take for both father and son to complete the same piece of work?
a) 6 2/5 days
b) 5 1/3 days
c) 7 ¾ days
d) 8 5/6 days
e) None of these
8) A alone can do a piece of work in x days. B alone can do the same work in 10 days more than A. C alone can do the same work in 10 days. If all of them working together and completed the work in 5 5/11 days, then find the value of ‘x’?
a) 20
b) 25
c) 30
d) 10
e) 12
9) M and N do a certain work in 42 days and 30 days respectively. N started the work alone and then after 6 days M joined him till the completion of the work. How long did the work last?
a) 16 days
b) 18 days
c) 20 days
d) 22 days
e) None of these
10) 15 men or 30 women or 45 children can complete the work in 12 days. Find the number of days taken by 8 men and 10 women and 15 children to complete the work?
a) 12 days
b) 5 days
c) 8 days
d) 10 days
e) None of these
Answers :
Directions (1-10) :
1) Answer: a)
Efficiency ratio of A and B = > 120: 100 = 6: 5
Day ratio of A and B = > 5: 6 (5x, 6x)
According to the question,
(1/5x) + (1/6x) = (11/60)
(6x + 5x) / (30x2) = (11/60)
11x / 30x2 = (11/60)
x = 2
The number of days taken by A alone to complete the work = 10 days
2) Answer: a)
Total work = men*days
Total units of work = 35*18 = 630 work
Work done in 8 days = 35*8 = 280 work
Remaining work = 630 – 280 = 350 work
Let the number of men left after 8 days be x,
According to the question,
350 / 14 = 35 – x
25 = 35 – x
x = 10
After 8 days from the start of the work, 10 men left the job.
3) Answer: a)
Men           Days          Work
40Â Â Â Â Â Â Â Â Â Â Â Â Â Â 15Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1
40Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3/5
?                 6                2/5
(40 * 9) / (3/5) = [(40 + x) * 6] / (2/5)
40 = 40 + x
x = 0
There is no extra man needed to complete the work.
4) Answer: b)
P = x days, Q = (x + 10) days
Given,
(1/x) + (1/(x + 10)) = 1/(6 2/3)
[x + x + 10] / [x (x + 10)] = 3/20(2x + 10) / (x2 + 10x) = 3/20
40x + 200 = 3x2 + 30x
3x2 – 10x – 200 = 0
x = 10, -6.66 (negative value will be eliminated)
So, x = 10
The efficiency ratio of P and Q = 1/10 : 1/20 = 2 : 1
5) Answer: d)
Total work = Men * days
12 m * 15 = 15 w * 24
1 m = 2 w
15 m + 20 w = 15 m + 10 m = 25 m
Men           days
12Â Â Â Â Â Â Â Â Â Â Â Â Â Â 15
25Â Â Â Â Â Â Â Â Â Â Â Â Â Â ?
(12 * 15) = (25 * x)
x = (12 * 15) / 25 = 36 / 5 = 7 1/5 days
6) Answer: b)
1 women’s 1 day wages = Total wages / (Number of days * total women)
= > 172500 / (46 * 25) = 150
1 men’s 1 day wages = 2 * 1 women’s 1 day wages = 2 * 150 = 300
Total men = 230400 / (24 * 300) = 32 men
7) Answer: b)
Efficiency ratio of father and son = 2 : 1
The day ratio of father and son = 1 : 2 (x, 2x)
2x = 16
x = 8
Father and Son’s one day work,
= > (1/8) + (1/16)
= > 3/16
Father and Son can complete a piece of work in,
= > 16/3 = 5 1/3 days
8) Answer: a)
Given,
(1/x) + (1/(x + 10)) + 1/10 = 11/60
(1/x) + (1/(x + 10)) = 11/60 – 1/10
(2x + 10) / (x2 + 10x) = 1/12
24x + 120 = x2 + 10x
x2 – 14x – 120 = 0
x = 20, -6 (Eliminate –ve value)
x = 20 days
9) Answer: c)
Work done by N in 6 days = (1/30) * 6 = 1/5
Remaining work = 1 – 1/5 = 4/5
(M + N)’s 1 day work = 1/42 + 1/30
= > (42 + 30) / (42 * 30)
= > 2/35
M and N together can complete the work in 35/2 days
So 4/5 work will be done by X and Y is,
= > (4/5) * (35/2)
= > 14 days
Total time taken = 14 + 6 = 20 days
10) Answer: d)
15 men = 30 women
1 men = 2 women
15 men = 45 children
1 men = 3 children
8 men + 10 women + 15 children = 8 men + 5 men + 5 men = 18 men
Men           days
15Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12
18Â Â Â Â Â Â Â Â Â Â Â Â Â Â ?
(15 * 12) = (18 * x)
x = (15 * 12) / 18 = 10 days
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