Question

A, B, and C enter into a business partnership by making investments in the ratio 3:5:7. After a year, C invests ₹ 33760 more while A withdraws ₹ 4560. The ratio of investments then changes to 24:59:167. How much does B invest?

• A. ₹ 22,000
• B. ₹ 22,400
• C. ₹ 22,980
• D. ₹ 23,600

Hint:

For partnership problems, express the investments in terms of a common variable and solve using the given ratios to find the unknown investment.

Answer 1

The Correct Option is D

Let the initial investments of A, B, and C be \(3x\), \(5x\), and \(7x\) respectively.
Step 1: Investments after the changes.
After 1 year, the investments of A, B, and C change. C invests ₹ 33760 more, and A withdraws ₹ 4560. So, their new investments are:
A's new investment = \(3x - 4560\)
B's new investment = \(5x\) (no change)
C's new investment = \(7x + 33760\)
The new ratio of investments is given as 24:59:167. So, we can write the equations:
\[ \frac{3x - 4560}{24} = \frac{5x}{59} = \frac{7x + 33760}{167}. \] Step 2: Solve for \(x\).
We now solve the equation for \(x\). Start with the first equation:
\[ \frac{3x - 4560}{24} = \frac{5x}{59}. \] Cross multiply:
\[ 59(3x - 4560) = 24(5x). \] Simplify:
\[ 177x - 269640 = 120x. \] \[ 57x = 269640. \] \[ x = \frac{269640}{57} = 4732.63. \] Step 3: Find B's investment.
Now that we know \(x\), B's initial investment is \(5x\):
\[ B's \, \text{investment} = 5 \times 4732.63 = 23663.15. \] Since the options are rounded to the nearest ₹ 100, the closest answer is ₹ 23,600.