Question:
Two persons X and Y started a business with investments in the ratio \(7:5\). After 3 months another person Z joined them with the respective ratio between the investments of Y and Z as \(3:4\). If the annual profit earned was Rs.20400, the difference between the X’s share and Z’s share in profit, in rupees, is
Two persons X and Y started a business with investments in the ratio \(7:5\). After 3 months another person Z joined them with the respective ratio between the investments of Y and Z as \(3:4\). If the annual profit earned was Rs.20400, the difference between the X’s share and Z’s share in profit, in rupees, is
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In partnership problems, always multiply investment by time first before finding the ratio.
Updated On: Jul 15, 2026
- \(2100\)
- \(2400\)
- \(2800\)
- \(3200\)
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The Correct Option is B
Solution and Explanation
Concept:
In partnership, profit sharing ratio depends on:
\[
\text{Investment} \times \text{Time}
\]
Step 1: Find the investment ratio.
Given: \[ X:Y=7:5 \] Let: \[ X=7k,\quad Y=5k \] Also: \[ Y:Z=3:4 \] So: \[ 5k:Z=3:4 \] \[ Z=\frac{20k}{3} \]
Step 2: Multiply by time.
X and Y invested for 12 months: \[ X=7k\times12=84k \] \[ Y=5k\times12=60k \] Z joined after 3 months, so invested for 9 months: \[ Z=\frac{20k}{3}\times9=60k \] Thus profit ratio: \[ 84:60:60 \] Simplify: \[ 7:5:5 \]
Step 3: Find each share.
Total ratio: \[ 7+5+5=17 \] Total profit: \[ 20400 \] Value of one part: \[ \frac{20400}{17}=1200 \] So: X’s share: \[ 7\times1200=8400 \] Z’s share: \[ 5\times1200=6000 \]
Step 4: Find the difference.
\[ 8400-6000=2400 \] Thus, the required answer is: \[ \boxed{2400} \]
Step 1: Find the investment ratio.
Given: \[ X:Y=7:5 \] Let: \[ X=7k,\quad Y=5k \] Also: \[ Y:Z=3:4 \] So: \[ 5k:Z=3:4 \] \[ Z=\frac{20k}{3} \]
Step 2: Multiply by time.
X and Y invested for 12 months: \[ X=7k\times12=84k \] \[ Y=5k\times12=60k \] Z joined after 3 months, so invested for 9 months: \[ Z=\frac{20k}{3}\times9=60k \] Thus profit ratio: \[ 84:60:60 \] Simplify: \[ 7:5:5 \]
Step 3: Find each share.
Total ratio: \[ 7+5+5=17 \] Total profit: \[ 20400 \] Value of one part: \[ \frac{20400}{17}=1200 \] So: X’s share: \[ 7\times1200=8400 \] Z’s share: \[ 5\times1200=6000 \]
Step 4: Find the difference.
\[ 8400-6000=2400 \] Thus, the required answer is: \[ \boxed{2400} \]
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