Question

If an amount of Rs.55500 is to be divided among X, Y and Z in the ratio 1/4: 1/5:1/6 then what is the difference between the amount received by X and Y?​

Answer 1

Step-by-step explanation:

Let the common multiplier of the given ratios be p.

Therefore,

Amount received by X $=\frac{1}{4}p$

Amount received by Y $= \frac{1}{5}p$

Amount received by Z $= \frac{1}{6}p$

$\therefore \: \frac{1}{4} p + \frac{1}{5} p + \frac{1}{6} p = 55500 \\ \\ \therefore \: (\frac{1}{4} + \frac{1}{5} + \frac{1}{6} )p = 55500 \\ \\ \therefore \: (\frac{15}{60} + \frac{12}{60} + \frac{10}{60} )p = 55500 \\ \\ \therefore \: \frac{37}{60} p = 55500 \\ \\ \therefore \:p = 55500 \times \frac{60}{37} \\ \\ \therefore \:p =1500 \times 60 \\ \\ \therefore \:p = 90000 \\ \\ Amount \: received \: by \: X \\ = \frac{1}{4} \times 90000 \\ =Rs. \: 22500 \\ \\ Amount \: received \: by \: Y \\ = \frac{1}{5} \times 90000 \\ =Rs. \: 18000 \\ \\ Amount \: received \: by \: Z \\ = \frac{1}{6} \times 90000 \\ =Rs. \: 15000$

Differece between the amounts received by X and Y = Rs. 22500 - Rs. 18000 = Rs. 4500