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 $\frac{1}{5}\times x=\frac{1}{3}\times (64-x)$
$\frac{x}{5}=\frac{64-x}{3}$
$3\times x=5\times (64-x)$
$3x=320-5x$
$8x=320$
$x=\frac{320}{8}=40$
Hence, A gets 40 coins
Number of coins received by B = 64 - x = 64 - 40 = 24