Question

Prasad’s monthly income is 25% more than that of Anam. Anam’s monthly income is 75% less than Bhushan. If the difference between the monthly income of prasad and Bhushan is Rs.26125, then what is Anam’s monthly income?
(A) Rs. 8000
(B) Rs. 16000
(C) Rs. 9500
(D) Rs. 10,000

Answer 1

Hint: Assume that the monthly income of Anam and Bhushan is Rs. x and Rs. y respectively. Prasad’s income is 25% more than that of Anam, so the monthly income of Prasad = Rs. (x+25% of x). Anam’s income is 75% less than that of Bhushan so, the monthly income of Anam = Rs. (y-75% of y). Now, compare the income of Anam and get the relation between x and y. The difference between the monthly income of prasad and Bhushan is Rs. 26125, \[y-\dfrac{5x}{4}=26125\] . Now, substitute y in terms of x and solve it further to get the value of x.

Complete step-by-step answer:
According to the question, we are given that Prasad’s monthly income is 25% more than that of Anam. Anam’s monthly income is 75% less than Bhushan.
First of all, let us assume that the monthly income of Anam is Rs. x …………………………………………(1)
Since Prasad’s income is 25% more than that of Anam so,
The monthly income of Prasad = Rs. (x+25% of x) = Rs. \[x+\dfrac{25x}{100}=\dfrac{125x}{100}=\dfrac{5x}{4}\] ………………………………………………(2)
Now, let us assume that the monthly income of Bhushan is Rs. y …………………………………………………..(3)
 Similarly, since Anam’s income is 75% less than that of Bhushan so,
The monthly income of Anam = Rs. (y-75% of y) = \[y-\dfrac{75y}{100}=\dfrac{25y}{100}=\dfrac{y}{4}\] ………………………………………………..(4)
But, from equation (1), we also have the monthly income of Anam.
Now, on comparing equation (1) and equation (4), we get
\[\Rightarrow x=\dfrac{y}{4}\]
\[\Rightarrow 4x=y\] ……………………………………………….(5)
From equation (2) and equation (3), we have the monthly income of prasad and Bhushan.
We are also given that the difference between the monthly income of prasad and Bhushan is Rs.26125.
Now, on subtracting equation (2) from equation (3), we get
\[\Rightarrow y-\dfrac{5x}{4}=26125\] ………………………………….(6)
Using equation (5) and on substituting \[y\] by \[4x\] in equation (6), we get
 \[\begin{align}
  & \Rightarrow 4x-\dfrac{5x}{4}=26125 \\
 & \Rightarrow \dfrac{16x-5x}{4}=26125 \\
 & \Rightarrow \dfrac{11x}{4}=26125 \\
 & \Rightarrow x=\dfrac{26125\times 4}{11} \\
\end{align}\]
\[\Rightarrow x=9500\] ……………………………………………(7)
From equation (1), we have the monthly salary of Anam equal to Rs. \[x\] and from equation (7), we have the value of \[x\] which is equal to 9500.
Therefore, the monthly income of Anam is Rs. 9500.
Hence, the correct option is (C).

So, the correct answer is “Option (C)”.

Note: We can also solve this question by only assuming the monthly salary of one person equal to \[x\] . Since this question is only a game of language. So, only assume the monthly salary of one person may create calculation mistakes and a little bit of a complex solution.