Question

Two persons A and B together have ₹6900. \(\frac{2}{5}\) of A's amount is equal to \(\frac{3}{4}\) of B's amount. Then the amount of B, in rupees, is:

• A. 4500
• B. 4200
• C. 3200
• D. 2400

Hint:

If two quantities are in the ratio \(m:n\) and their sum is \(S\), then the quantities are \(\frac{m}{m+n}S\) and \(\frac{n}{m+n}S\).

Answer 1

The Correct Option is D

Concept: Use the given fractional relation to obtain the ratio of the two amounts and then divide the total amount in that ratio.

Step 1: Finding the ratio A:B.
\[ \frac{2}{5}A=\frac{3}{4}B \] Multiplying both sides by 20, \[ 8A=15B \] \[ A:B=15:8 \]

Step 2: Using the total amount.
\[ A+B=6900 \] Total ratio parts \[ 15+8=23 \] Value of one part \[ \frac{6900}{23}=300 \]

Step 3: Calculating B's amount.
\[ B=8\times300=2400 \] {2400}