Question

Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing 4000 and 6000 respectively. The conditions of partnership were as follows:
1. In case of profits till 200,000 per annum, profits would be shared in the ratio of the invested capital.
2. Profits from 200,001 till 400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
3. Profits in excess of 400,000, Shyam would take 35% out of the profits beyond 400,000, before the division of remaining profits, which will then be based on ratio of invested capital.
If Shyam’s share in a particular year was 367000, which option indicates the total business profit (in ₹) for that year?

• A. 520,000
• B. 530,000
• C. 540,000
• D. 550,000
• E. None of the above

Hint:

Handle slab-wise profit sharing by computing each slab separately and summing.
When a fixed percentage is taken out first, apply the capital-ratio split only to the remainder.

Answer 1

The Correct Option is D

Step 1: Capital ratio (Ram : Shyam) \(=4000:6000=2:3\). Hence, when distributed by capital, Shyam’s share is \(\frac{3}{5}\) of the distributable amount.
For the first \(₹ 200{,}000\): Shyam gets \(\frac{3}{5}\times 200{,}000=120{,}000\).
For the next \(₹ 200{,}000\): Shyam first takes \(20%\) of this slab \(=0.20\times 200{,}000=40{,}000\). The remaining \(₹ 160{,}000\) is shared \(2:3\), so Shyam gets \(\frac{3}{5}\times 160{,}000=96{,}000\).
Thus, up to \(₹ 400{,}000\), Shyam has \(120{,}000+96{,}000+40{,}000=256{,}000\). Step 2: Let profit beyond \(₹ 400{,}000\) be \(x\). From this excess, Shyam gets \[ 0.35x+\frac{3}{5}\times(0.65x)=0.35x+0.39x=0.74x. \] Given Shyam’s total share is \(₹ 367{,}000\): \[ 256{,}000+0.74x=367{,}000 \ \Rightarrow\ 0.74x=111{,}000 \ \Rightarrow\ x=\frac{111{,}000}{0.74}=150{,}000. \] Step 3: Therefore, the total profit \(=400{,}000+x=400{,}000+150{,}000=\boxed{₹ 550{,}000}\).