Question

$A$ and $B$ have $460$ coins altogether. If $\frac{3}{4}$ of $A$'s number of coins is equal to $\frac{2}{5}$ of $B$'s number of coins, find how many coins must $B$ give to $A$, so that they both have equal number of coins.

• A. $50$
• B. $70$
• C. $20$
• D. $90$

Answer 1

Answer: (B)

$70$

Let $A$'s number of coins $=$ $x$, so $B$'s number of coins $=$ $460-x$

$\frac{3}{4}$ of $A$ $=\frac{2}{5}$ of $B$

$\frac{3}{4}x=\frac{2}{5}(460-x)$

$\therefore 15x=8(460-x)15x=3680-8x23x=3680x=160$

$A$'s number of coins = $160$ coins

$B$'s number of coins = $460-x=300$ coins

So, $B$ has to give $A$, $70$ coins, so they both have equal number of coins. which is $230$ coins each.