Question

Alfred and Rani both picked different two digit numbers. If you multiply Alfred's number by $5$ and double Rani's number, the sum is $300$. If you double Alfred's number and multiply Rani's number by $3$, the sum of the two numbers is $252$. What is the sum of their two numbers?

• A. $96$
• B. $112$
• C. $128$
• D. $144$

Answer 1

Answer: (A)

$96$

Let Alfred take $x$ and Rani take $y$.
As per given question,
$5x+2y=300$.......(1)
$2x+3y=252$......(2)
On multiplying (1) with $3$ and equation (2) with $2$, we get
$15x+6y=900$
$\to 4x+6y=504$
On subtracting both, we get
$15x+6y=900$
$4x+6y=504$
______________________
$11x=396$
$\Rightarrow x=36$
Putting $x=36$ in (1), we get
$5\times 36+2y=300$
$\Rightarrow 2y=300-180$
$\Rightarrow 2y=120$
$\Rightarrow y=60$
Sum of two numbers is $60+36=96$.