Question

If three times the larger of the two numbers is divided by the smaller one, we get $4$ as quotient and $3$ as the remainder. Also, if seven times the smaller number is divided by the larger one, we get $5$ as quotient and $1$ as remainder. Find the sum of the numbers

• A. $34$
• B. $43$
• C. $47$
• D. $74$

Answer 1

The correct option is B $43$

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

We use the division statement that
$\text{Dividend =(Divisor x Quotient) + Remainder}$

So, in the first case,

$3x=4y+3$

$\Rightarrow 4y=3x-3$ ...........(i)

And $7y=5x+1$ .............(ii).

Multiplying (i) by $7$ & (ii) by $4$, we get

$28y=21x-21$ ......(iii) and

$28y=20x+4$ .....(iv).

Subtracting eq (iv) from (iii) we get,

$x-25=0$

$\Rightarrow x=25$

$\Rightarrow 4y=3\times 25-3=72$

$\therefore y=\frac{72}{4}=18$

$\Rightarrow x+y=25+18=43$