Question

A invested Rs 5500 for 2 months more than B while B invested Rs 4000 for 1 month more than C who invested Rs 5600. If out of a total profit of Rs 6000, the difference in the shares of C and B is Rs 250 then find the time for which A invested the money

Answer 1

Let C invested money for $x$ months,

then B for $(x+1)$ months,

then A for $(x+1+2)=(x+3)$ months

So ratio of shares of A : B : C is,

$\Rightarrow 5500\times (x+3):4000\times (x+1):5600\times x$

$\Rightarrow 55(x+3):40(x+1):56x$

Total profit is $6000$ Rs.

Thus by given condition,

$\Rightarrow \frac{56x-(40x+40)}{55x+165+40x+40+56x}\times 6000=250$

$\Rightarrow \frac{16x-40}{151x+205}\times 6000=250$

$\Rightarrow \frac{16x-40}{151x+205}\times 24=1$

$\Rightarrow 384x-960=151x+205$

$\Rightarrow 233x=1165$

$\Rightarrow x=5$

So A invested for $5+3=8$ months