Question

ratul and pratual together can complete a task in 18 days they start the task together but ratul had to leave in 7 days before the work got over as a result it took of 23 days to complete the task how many days would it have taken parul to complete the work by himself​

Answer 1

Answer:

63 days

Step-by-step explanation:

Let Ratul completes in 1 day = 1/x work

Let Pratul completes in 1 day = 1/y work

Work done by Ratul and Pratul in 18 days = 18(1/x + 1/y)

$18(\frac{1}{x}+\frac{1}{y})=1$

or, $\frac{1}{x}+\frac{1}{y}=\frac{1}{18}$    ..................(1)

Also, when Ratul leaves after 16 days, Pratul completes the work in another 7 days

Hence

$16(\frac{1}{x}+\frac{1}{y})+\frac{7}{y}=1$

$\implies \frac{16}{x}+\frac{23}{y}=1$      ............. (2)

Multiplying eq (1) by 16 and subtracting it from eq (2)

$\frac{23}{y}-\frac{16}{y}=1-\frac{16}{18}$

$\implies \frac{7}{y}=\frac{1}{9}$

$\implies y=7\times 9$

$\implies y=63$

Therfore, Pratul will complete the work in 63 days all by himself.