Question

A profit of Rs 6000 is to be distributed among A, B, and C in the ratio $3:4:5$ respectively. How much more will C get than B?
a) Rs 500
b) Rs 1200
c) Rs 2000
d) Rs 2500

Answer 1

Hint: Let us assume that ‘x’ be the profit shared by each A, B, and C in the ratio $3: 4: 5$. So, we can say that A’s share is 3x of Rs 6000, B’s share is 4x of Rs 6000, and C’s share is 5x of Rs 6000. Using this relation, find the value of x. Then, find the share of B and C and subtract the value of the share of B from C to get to know how much more C will get than B.

Complete step-by-step solution
We know that a profit of Rs 6000 is to be distributed among A, B, and C in the ratio $3:4:5$ respectively.
As we have assumed, that ‘x’ be the profit shared by each A, B and C
So, we get: $3x+4x+5x=6000......(1)$
Now, get the value of x from equation (1)
We have:
$\begin{align}
  & \Rightarrow 12x=6000 \\
 & \Rightarrow x=Rs.500......(2) \\
\end{align}$
Now, find the profit shared by B and C, we get:
Profit shared by B: $\Rightarrow 4x=4\times 500=Rs.2000$
Profit shared by C: $\Rightarrow 5x=5\times 500=Rs.2500$
Now, subtract the value of share of B from C, we get:
$\begin{align}
  & \Rightarrow 2500-2000 \\
 & \Rightarrow Rs.500 \\
\end{align}$
Hence, C will get Rs. 500 more than B.

Note: Whenever two quantities are given in ratio, it doesn’t mean that the value of the quantity is equal to the given ratio.
For example:
If $a:b=3:5$, it doesn’t mean that a = 3 and b = 5.
Instead, assume that $a=3x$ and $b=5x$ where ‘x’ is a constant.