Question

A, B and C invest in the ratio of 3:4:5. The percentage of return on their investments is in the ratio of 6:5:4. Find the total earnings, if B earns Rs 250 more than A.

Answer 1

Hint: As you observe in the question, the investments of A,B and C are given as a ratio. Also the percentage of return on their investments is given in ratio form. We have to consider the percentage return of each on their investment separately. The earning can be calculated by finding out the return after their investment. We can use the relation between A and B’s earnings given in the question, which is earning of A + Rs 250 = Earning of B.

Complete step by step solution:For A:
6% return is obtained on investment of 3x. Thus earning is \[\dfrac{6}{{100}} \times 3x\] or $0.06\times3x$
For B:
5% return is obtained on investment of 4x. Thus earning is\[\dfrac{5}{{100}} \times 4x\] or \[0.05 \times 4x\]
Now the relation between A and B’s earnings is given as:
Earnings of A + 250 = Earning of B
\[ \Rightarrow \dfrac{6}{{100}} \times 3x + 250 = \dfrac{5}{{100}} \times 4x\]
\[ \Rightarrow \dfrac{{18x - 20x}}{{100}} = - 250\]
\[ \Rightarrow \dfrac{{ - 2x}}{{100}} = - 250\] (the negative sign on both sides get cancelled)
\[ \Rightarrow 2x = 250 \times 100\]
\[ \Rightarrow x = \dfrac{{250 \times 100}}{2}\]
\[ = Rs12,500\]
Therefore the value x is Rs 12,500
Thus earning of A is \[\dfrac{6}{{100}} \times 3x\]
\[\begin{gathered}
   = \dfrac{6}{{100}} \times 3 \times 12500 \\
   = Rs2,250 \\
\end{gathered} \]
Earning of B is \[\dfrac{5}{{100}} \times 4x\]
\[\begin{gathered}
   = \dfrac{5}{{100}} \times 4 \times 12500 \\
   = Rs2,500 \\
\end{gathered} \]
Earning of C \[\dfrac{4}{{100}} \times 5x\]
\[\begin{gathered}
   = \dfrac{4}{{100}} \times 5 \times 12500 \\
   = Rs2,500 \\
\end{gathered} \]


Note: Students must keep in mind that they have to calculate the percentage return on the investments given in order to find the earnings of A, B and C. Also the value of B’s earning is Rs 250 more than A, thus fulfilling the requirements of the question. If you practice similar questions your concept of such problems will get stronger. The calculation part is fairly easy.