Question

P and Q can do a piece of work in 12 days,Q and R can do a piece of work in 18 days and R and P can do piece of work in 15 days.in how many days R alone can do the same work?​

Answer 1

Step-by-step explanation:

Given,

★P and Q can do a piece of work in 12days.

★Q and R can do a piece of work in 18 days.

★R and P can do a piece of work in 15days.

To Find :-

In how many days R alone can do the work .

Solution:-

Let,

the work done by P = P days

the work done by Q = Q Days

the work done by R = R days

According to Question :-

1) P and Q can do a piece of work in 12days

$\sf\implies$ One work done by both P and Q together = 1/12 day

P + Q = 1/12

2) Q and R can do a piece of work in 18 days.

$\sf\implies$ One work done by both R and Q together = 1/18 day

R + Q = 1/18

3) R and P can do a piece of work in 15days.

$\sf\implies$ One work done by both R and P together = 1/15 day

P + R = 1/15

Adding all the equations what we have got :-

P + Q + R + Q + P + R = 1/12 + 1/18 + 1/15

$2P + 2Q + 2R = \dfrac{15}{180} + \dfrac{10}{180} + \dfrac{12}{180}$

Since , L.C.M of 12 , 18 , 15 = 180

$2(P+Q+R) = \dfrac{15 + 10 + 12}{180}$

$2(P+Q+R) = \dfrac{37}{180}$

$P+Q+R = \dfrac{37}{360}$

$\dfrac{1}{12} + R = \dfrac{37}{360}$

$R = \dfrac{37}{360} - \dfrac{1}{12}$

$R = \dfrac{37}{360} - \dfrac{30}{360}$

R = $\sf\dfrac{37-30}{360}$

R = 7/360

Therefore work done by R in one day = 7/360

Total work done by 'R' alone = 1/7/360 = 360/7

≈ 51.4 days