AMCAT Quantitative Ability Previous Papers-12

A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
35 ½
36 ½
37 ½
38 ½

Answer: Option C

Explanation:

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 —(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 (1/2) days

Ques. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?
30 days
40 days
50 days
60 days

Answer: Option B

Explanation:

Let 1 man’s 1 day work = x
and 1 woman’s 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]

10 women 1 day work = 10/400 = 1/40

10 women will finish the work in 40 days

Ques, 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
6 days
7 days
8 days
9 days

Answer: Option B

Explanation:

1 woman’s 1 day’s work = 1/70
1 Child’s 1 day’s work = 1/140
5 Women and 10 children 1 day work =

(5/70 +10/140)=1/7

So 5 women and 10 children will finish the work in 7 days.

Ques. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
1:2
1:3
2:1
2:3

Answer: Option C

Explanation:

Let 1 man 1 day work = x
1 boy 1 day work = y

then 5x + 2y = 4(x+y)
=> x = 2y
=> x/y = 2/1
=> x:y = 2:1

Rahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?
84 days
82 days
76 days
68 days

Answer: Option A

Explanation:

As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) – (Rahul one day work)
=1/35−1/60=1/84

Hence Sham will complete the given work in 84 days.

Ques. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

A.    4 days
B.    5 days
C.    6 days
D.    7 days
Answer: Option A

Explanation:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

Then, 6x + 8y =    1/10   and 26x + 48y =    1/2 .

Solving these two equations, we get : x =    1/100    and y =    1/200    .
(15 men + 20 boy)’s 1 day’s work =        15/100    +    20/200        =    1/4    .
15 men and 20 boys can do the work in 4 days.