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- 56. 6 dogs and 8 cats do a work in 12 days, while 5 dogs and 8 cats finish it in 16days, 4dogs and 8 cats will finish it in.
A.14 days
B.20 days
C.24 days
D.12 days
Answer & Explanation
Answer: Option C 
(6dogs+8cats) 1 day work = 1/12
(5dogs+8cats) 1 day work = 1/16
substract 1 and 2
i.e 1/12 – 1/16= 1/48
i.e 1 dog 1 day work is 1/48
4dogs + 8cats 1day work is 1/16 – 1/48 = 1/24
thus 4 dogs and 8 cats will finish it in 24 days
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- 57. A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
A.30 days
B.35 days
C.40 days
D.45 days
Answer & Explanation
Answer: Option A
Let ‘x’ be the number of days taken by B alone to finish the whole work
Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days.
Then, working together,
3x/2 × x/3x/2 + x = 18 days
3x × x/5x = 18
3x/5 = 18
Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days.
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- 58. A and B can finish a piece of work in 12 days and 18 days respectively. A begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in
A.14 1/3 days
B.15 2/3 days
C.16 1/3 days
D.18 2/3 days
Answer & Explanation
Answer: Option A
Both of them together can finish the work (daily working) in 12 × 18/30 days = 36/5
= 7 1/5 days.
By working in alternate days, their 2 day’s work = 5/36
Their, 14 day’s work (because they take more than double of 7 days) = 5/36 × 7
= 35/36
Remaining work = 1 – 35/36 = 1/36
Because A started the work, the remaining work is finished by A
A’s 1 day’s work = 1/12
Therefore, the No. of days taken by A to finish 1/36 work = 1/36/1/12 = 1/3 days.
Therefore, the total work is completed in 14 + 1/3 = 14 1/3 days.
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- 59. A can do a piece of work in 14 days which B alone can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days for the work to be completed is
A.6 3/5 days
B.8 ½ days
C.10 1/5 days
D.13 ½ days
Answer & Explanation
Answer: Option C
B’s 1 day’s work = 1/21
B’s 3 day’s work = 1/21 ×3 = 1/7
The remaining work finished by both of them = 1 – 1/7 = 6/7
Both together can finish it in 14 × 21/35 days = 42/5 days
Their, 1 day’s work = 5/42
Therefore, the No. of days taken by them together to finish 6/7 work
= 6/7/5/42 = 6/7 × 42/5 = 36/5 = 7 1/5 days
Therefore, the total No. of days for the work to be completed = 3 + 7 1/5 = 10 1/5 days.
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- 60. A and B can finish a piece of work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days. A alone can finish the work in
A.48 days
B.50 days
C.54 days
D.60 days
Answer & Explanation
Answer: Option D
(A + B)’s 1 day’s work = 1/30
Their 20day’s work = 1/30 × 20 = 2/3
Remaining 1/3 work is done by A in 20 days
Therefore, A alone can finish the work in 3 × 20 = 60 days.
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