Question

64 gold coins must be distributed between 2 people (A and B) such that ${\frac{1}{5}}^{th}$ of the number of gold coins received by A is equal to ${\frac{1}{3}}^{rd}$ of the number of gold coins received by B. What is the number of gold coins received by A and B?

• A. A - 44, B - 20.
• B. A - 22, B - 42
• C. A - 48, B - 16
• D. A - 40, B - 24

Answer 1

The correct option is D A - 40, B - 24

If the number of coins received by A is taken as x, then the number of coins received by B will be 64 - x.
Now we know that ${\frac{1}{5}}^{th}$ of the number of coins received by A is equal to ${\frac{1}{3}}^{rd}$ of the number of coins received by B,
Hence $\frac{1}{5}\times x=\frac{1}{3}\times (64-x)$
$\Rightarrow \frac{x}{5}=\frac{64-x}{3}$
$\Rightarrow 3\times x=5\times (64-x)$
$\Rightarrow 3x=320-5x$
$\Rightarrow 8x=320$
$\Rightarrow x=\frac{320}{8}=40$
Hence, A gets 40 coins
Number of coins received by B = 64-x = 64 - 40 = 24.