### Question 5

SSC-CGL 2020 Mar 4 Shift 2

A can complete a work in (d + 8) days and B can complete the same work in (d + 18) days. Working together, they can complete this work in d days. What is the value of d?

### Solution in Short

Remember Shortcut: If A and B together complete a work in X days, and A in X + a, and B in X + b, then X² = a x bBy the above shortcut, d² = 8 x 18 = 144, so d = 12 ans!

### Solution in Detail

let work = $\displaystyle (d + 8)(d + 18)\text{. . . (1)}$

NOTE: why we took it thus? As taught in our elementary math books, we could take total work as 1, or even any variable like W. But calculations can be simplified if we take it as LCM or as the product of the days taken by each worker to complete the work.A completes in $\displaystyle (d + 8)$ days(given)

$\displaystyle \therefore$ A's 1 day work = $\displaystyle \frac{(d + 8)(d + 18)}{d + 8}$

$\displaystyle \therefore $ = $\displaystyle (d + 18)$

likewise, of B = $\displaystyle (d + 8)$

A + B total 1 day work = $\displaystyle (d + 8) + (d + 18)$ = $\displaystyle 2(d + 13)$. It is given that they take $\displaystyle d$ days to complete the work. So the total work they do together is:

$\displaystyle d \times [2(d + 13)] = 2d(d+13)$

Equating to the total work (1),

$\displaystyle 2d(d + 13) = (d + 8)(d + 18)$

Simplifying, $\displaystyle d = 12\:\underline{Ans}$

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