Question

If $3$ times of a larger number is divided by a smaller number the quotient is $4$ and remainder is $3$ and when $7$ times of the smaller number is divided by the larger number then quotient is $5$ and remainder is $1$. Find the two numbers.

• A. $16,27$
• B. $18,25$
• C. $20,28$
• D. $22,33$

Answer 1

The correct option is B $18,25$

Let the larger number be $x$ and the smaller number be $y$.

According to question, we have;

$3x=4y+3\Rightarrow x=\frac{4y+3}{3}$

$7y=5x+1$

$=>7y=\frac{5(4y+3)}{3}+1$

$=>21y=20y+15+3$

$=>y=18$

$3x=4\times 18+3$

$=>x=25$

Larger number $=25$

Smaller number $=18$