Question

A and B can do a piece of work in 12 days, C and A in
20 days and B and c
in 15 days, then in how many days will they finish it working together 2
(a) 20 days (b) 5 days (c) 15 days
(d) 10 days
​

Answer 1

Correct Answer

Option (d) 10 days.

Before we solve

If they work together, their work rate is added. So we're first going to find their work rate.

Solution

Let the work rate of three people be a, b, and c.

Then,

• $a+b=\dfrac{1}{12}$
• $b+c=\dfrac{1}{15}$
• $c+a=\dfrac{1}{20}$

Let's add all the equations.

$\rightarrow 2(a+b+c)=\dfrac{5+4+3}{60}=\dfrac{12}{60}$

$\rightarrow 2(a+b+c)=\dfrac{12}{60} =\dfrac{1}{5}$

$\rightarrow a+b+c=\dfrac{1}{10}$ (Work per Day)

Hence, $\dfrac{1}{a+b+c} =10$ (Days per Work)

Hence, if all people do a piece of work, they will spend 10 days.

Answer 2

Given :-

A,B   can do a piece of work in 12 days, C and A in

20 days and B and c  in 15 days,

To Find :-

In how many days will they finish it working together 2

Solution :-

Here,

$\bf A + B =\dfrac{1}{12}$

$\bf C +A = \dfrac{1}{20}$

$\bf B + C = \dfrac{1}{15}$

They all are repeating 2 times So,

$\sf 2a + 2b + 2c = \dfrac{1}{12}+ \dfrac{1}{20}+ \dfrac{1}{15}$

Taking 2 as common

$\sf 2(a+b+c) =\dfrac{5+4+3}{60}$

$\sf a +b+c = \dfrac{12}{60}$

$\sf a +b+ c = \dfrac{1}{5}$

Now multiplying by 1/2

$\bf\dfrac{1}{5} \times \dfrac{1}2$

1/10

On reciprocal

10 dyas