Question

$A$ and $B$ have some coins. If $A$ gives $100$ coins to $B$, then $B$ will have twice the number of coins left with $A$. Instead if $B$ gives $40$ coins to $A$, then $A$ will have thrice the number of coins left with $B$. How many more coins does $A$ have than $B$?

• A. $212$
• B. $186$
• C. $124$
• D. $88$

Answer 1

The correct option is D $88$

Let the number of coins with $A=a$ and with $B=b$.
For the given statements,
$2(a-100)=b+100$
$\Rightarrow 2a-200=b+100$
$\Rightarrow 2a-b=300$ ....(1)
And $a+40=3(b-40)$
$\Rightarrow a+40=3b-120$
$\Rightarrow a-3b=-160$ ....(2)
Solving equations (1) and (2), we get
$a=212;b=124$
So, $A$ has $a-b=212-124=88$ coins more than $B$.