Question

The ratio of work done by (x-1) men in (x+1) days to that of (x+2) men in (x-1) days is 9:10, find the value of x.

Answer 1

Let the work done by one man in one day be : W

$:\implies$  Work done by (x - 1) men in one day = W(x - 1)

$:\implies$  Work done by (x - 1) men in (x + 1) days = W(x - 1)(x + 1)

$:\implies$  Work done by (x + 2) men in one day = W(x + 2)

$:\implies$  Work done by (x + 2) men in (x - 1) days = W(x + 2)(x - 1)

Given - Ratio of work done by (x - 1) men in (x + 1) days to that of (x + 2) men in (x - 1) days is 9 : 10

$\mathsf{:\implies \dfrac{W(x - 1)(x + 1)}{W(x + 2)(x - 1)} = \dfrac{9}{10}}$

$\mathsf{:\implies \dfrac{(x + 1)}{(x + 2)} = \dfrac{9}{10}}$

$:\implies$  10(x + 1) = 9(x + 2)

$:\implies$  10x + 10 = 9x + 18

$:\implies$  10x - 9x = 18 - 10

$:\implies$  x = 8

Answer 2

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(x-1)(x+1):(x+2)(x-1)=9:10

cross multiply them

10x^2-10=9x^2+9x-18

simplifying

x^2-9x+8=0

solving it, we get

(x+1)(x-8)=0

so the answer is 8 i.e. option 5