Question

A and B both have some pencils. If A gives $10$ pencils to B, then B will have twice as many as A. And if B gives $10$ pencils to A, then they will have the same number of pencils. How many pencils does each has?

• A. A = $20$ and B = $55$
• B. A = $20$ and B = $60$
• C. A = $30$ and B = $50$
• D. A = $50$ and B = $70$

Answer 1

The correct option is D A = $50$ and B = $70$

Let A has $x$ pencils and B has $y$.

As per the statement, "If A gives 10 pencils to B, then B will have twice as many as A":

$⟹2(x-10)=y+10$

$2x-y=30$ --- (1)
Also, as per the statement, "if B gives 10 pencils to A, then they will have the same number of pencils"

$⟹x+10=y-10$

$x-y=-20$ --- (2)

Subtracting equation $\left(2\right)$ from $\left(1\right)$, we get:

$2x-y-x+y=30+20$

$x=50$

Substituting $x=50$ in equation $\left(2\right)$, we get:

$50-y=-20$

$⟹y=70$

So, A has $50$ pencils and B has $70$ pencils.