Question Detail

A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in

\begin{aligned} 13\frac{1}{4} \end{aligned}
\begin{aligned} 13\frac{1}{2} \end{aligned}
\begin{aligned} 13\frac{3}{4} \end{aligned}
\begin{aligned} 13\frac{4}{4} \end{aligned}

Answer: Option C

Explanation:

A's 1 day work = 1/16
B's 1 day work = 1/12

As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48

[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]

Work done in 6 pairs = 6*(7/48) = 7/8

Remaining work = 1-7/8 = 1/8

On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16

On 14th day it is B turn,

1/12 work done by B in 1 day

1/16 work will be done in (12*1/16) = 3/4 day

So total days =
\begin{aligned} 13\frac{3}{4} \end{aligned}

It may be a bit typical question, but if are not getting it in first try then give it a second try. Even not, then comment for explanation for this. We will be happy to help you.

1. 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

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

2. A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in

\begin{aligned} 13\frac{1}{4} \end{aligned}
\begin{aligned} 13\frac{1}{2} \end{aligned}
\begin{aligned} 13\frac{3}{4} \end{aligned}
\begin{aligned} 13\frac{4}{4} \end{aligned}

Answer: Option C

Explanation:

3. To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will take

24 days
16 days
12 days
8 days

Answer: Option D

Explanation:

A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6

We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)

So A 1 day work =
\begin{aligned}
\frac{1}{6}- \frac{1}{12} \\
= \frac{1}{12}
\end{aligned}

Similarly C 1 day work =
\begin{aligned}
\frac{1}{6}- \frac{1}{8} \\
= \frac{4-3}{24} \\
= \frac{1}{24}
\end{aligned}

So A and C 1 day work =

\begin{aligned}
\frac{1}{12} + \frac{1}{24} \\
= \frac{3}{24} \\
= \frac{1}{8}
\end{aligned}

So A and C can together do this work in 8 days

4. 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?

\begin{aligned} 35\frac{1}{2} \end{aligned}
\begin{aligned} 36\frac{1}{2} \end{aligned}
\begin{aligned} 37\frac{1}{2} \end{aligned}
\begin{aligned} 38\frac{1}{2} \end{aligned}

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

5. A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

\begin{aligned} 7\frac{1}{2}days \end{aligned}
\begin{aligned} 6\frac{1}{2}days \end{aligned}
\begin{aligned} 5\frac{1}{2}days \end{aligned}
\begin{aligned} 4\frac{1}{2}days \end{aligned}

Answer: Option A

Explanation:

In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,

Son's one day work =
\begin{aligned}
\left(\frac{1}{3}-\frac{1}{5} \right) \\
=\left(\frac{5-3}{15} \right) \\
= \frac{2}{15}
\end{aligned}

So son will do whole work in 15/2 days
which is =

\begin{aligned} 7\frac{1}{2}days \end{aligned}

mylan murugesan 7 years ago

in the first question,why we have to do the sum till 14th turn???
please explain
job seeker 7 years ago

in first question till 3/4 is clear bt howcome 13 3/4 is coming
Nirmal Epaenetu Parusu 7 years ago

iam unable to understand the 1st one can u plz explain it elaborately???
Nirmal Epaenetu Parusu 7 years ago

can u plz explain it elaborately?
Sourav Sekhar Mohanty 8 years ago

i cant understand the question .please any one help me
Shrinivas Rao 8 years ago

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Shrinivas Rao 8 years ago

A and B can do a work in 6 days, A and C in 5n half days. B and C in 4 days, in how many days A alone can do it???
anu 10 years ago

sory 2 say bt i didnt get it.
i understood d steps til ,trick
my email id:[email protected]
yashasvi 11 years ago

I am unable to understand this explanation