Question

If the sum of two numbers is divided by $15$, the quotient is $2$ and the remainder is $10$. If the difference of the same numbers is divided by $3$ then the quotient is $4$ and the remainder is $2$. Find the numbers.

Answer 1

Let $x$ and $y$ be the two numbers such that $x>y$.

We know that,

Dividend $=$ Divisor $\times$ Quotient $+$ Remainder

Now, according to the question,

$x+y=15\times 2+10$

$\Rightarrow x+y=40.....\left(1\right)$

Also,

$x-y=3\times 4+2$

$\Rightarrow x-y=14.....\left(2\right)$

Adding equation $\left(1\right)\&\left(2\right)$, we have

$(x+y)+(x-y)=40+14$

$\Rightarrow 2x=54$

$\Rightarrow x=\frac{54}{2}=27$

Substituting the value of $x$ in equation $\left(1\right)$, we have

$27+y=40$

$\Rightarrow y=40-27=13$

Hence, the two numbers are $27$ and $13$.