Question

Ratio of incomes of A, B and C last year was 3:4:5. The ratio of their individual incomes of last year and this year are 4:5, 2:3 and 3:4 respectively if the sum of their present income is Rs. 78800. Find the present individual income of B?
A) Rs 18000
B) Rs 32000
C) Rs 28800
D) Cannot be determined

Answer 1

Hint: Take present income of A, B and C as a, b and c respectively. And the last year income of A, B and C is 3x, 4x and 5x. Now, take the ratio last year and present year income then equate it to the given ratios. You will get a, b and c in terms of x then write a + b + c = 78800 and solve for x.
Complete step-by-step answer:
Let us assume present income of A, B and C as a, b and c.
The ratios of last year income for A, B and C is given as 3:4:5. Then the last year incomes of A, B and C can be 3x, 4x and 5x, where x is constant.
The ratio of last year and present income of A is shown below:
$\begin{align}
  & \dfrac{3x}{a}=\dfrac{4}{5} \\
 & \Rightarrow a=\dfrac{15x}{4} \\
\end{align}$
The ratio of last year and present income of B is shown below:
$\begin{align}
  & \dfrac{4x}{b}=\dfrac{2}{3} \\
 & \Rightarrow b=6x \\
\end{align}$
The ratio of last year and present income of C is shown below:
$\begin{align}
  & \dfrac{5x}{c}=\dfrac{3}{4} \\
 & \Rightarrow c=\dfrac{20x}{3} \\
\end{align}$
Sum of present incomes of A, B and C is 78800.
a + b + c =78800
Substituting the values of a, b and c in the above equation we get,
$\begin{align}
  & \dfrac{15x}{4}+6x+\dfrac{20x}{3}=78800 \\
 & \Rightarrow \dfrac{45x+72x+80x}{12}=78800 \\
 & \Rightarrow x=\dfrac{78800\times 12}{197} \\
 & \Rightarrow x=4800 \\
\end{align}$
The present income of B is b and we have shown above that b = 6x so b =6 $\times$ 4800 = 28800
Hence, the correct option is (C).
Note: In the above problem we have converted 3:4:5 into 3x, 4x and 5x. As 3:4:5 is the smallest form of the numbers left after some common number gets cancelled among the three numbers and as we don’t know the common number so we have taken that common number as “x” and multiplied it with the ratio.