Question

Rs. 350 is divided among P, Q and R in the ratio 2:5:3. Find the amount of money that the child with the largest share got.
A. Rs. 175
B. Rs. 180
C. Rs. 145
D. Rs. 160

Answer 1

Hint: Convert the ratio in which the money was divided into fractions. Clearly, the child with the largest fraction will get the largest share of the money. Thus, obtain the largest share by multiplying the fraction with the total money in hand.
Complete step-by-step solution -
The ratio in which Rs. 350 is divided among P, Q and R = 2:5:3
Thus, P will get \[\dfrac{2}{2+\text{5+3}}\text{ = }\dfrac{2}{10}\] share of the money.
Q will get \[\dfrac{5}{2+\text{5+3}}\text{ = }\dfrac{5}{10}\] share of the money.
R will get \[\dfrac{3}{2+\text{5+3}}\text{ = }\dfrac{3}{10}\] share of the money.
Clearly, it can be seen that Q has got the largest fraction, i.e. $\dfrac{5}{10}$ of Rs. 350. Hence, Q has received the largest share of money.
$\therefore $ Share of money received by Q
$\begin{align}
  & =\text{ }\dfrac{5}{10}\text{ of Rs}\text{. 350} \\
 & =\text{ Rs}\text{. }\left( \dfrac{1}{2}\text{ x 350} \right) \\
 & =\text{ Rs}\text{. 175} \\
\end{align}$
Thus, Q received the largest share of money of Rs. 175.
Hence, the correct answer is option A.

Note: One can also find who has got the largest share simply by looking at the ratio, who has the highest proportion among the three children. P, Q and R have received money in the ratio 2:5:3, it can be seen that Q has got the highest proportion among the three of them. S0, Q has got the largest share of money.