XAT 2012 — QA & DI Question 27
Answer the following question based on the information given below.
The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.
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Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing Rs. 4000 and Rs. 6000 respectively. The conditions of partnership were as follows:
- In case of profits till Rs. 200,000 per annum, profits would be shared in the radio of the invested capital.
- Profits from Rs. 200,001 till Rs. 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.
- Profits in excess of Rs. 400,000, Shyam would take 35% out of the profits beyond Rs. 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 Rs. 367000, which option indicates the total business profit (in Rs.) for that year?
Answer & solution
- A
520,000
- B
530,000
- C
540,000
550,000
- E
None of the above
For first Rs. 200000, Shyam gets, 6000/(4000 + 6000) × 100 = 60% of the profit.
For next Rs. 200000, he gets 20% + plus 60% of the remaining profit.
i.e. 20% + 80 × 0.6% = 68%
Similarly, for a profit margin greater than Rs. 400000, he will get, 35% + 65 × 0.6% = 74% of the profits beyond Rs. 400000
Now, for a profit of first Rs. 400000, Shyam will receive 200000 × (68 + 60)/100 = 256000
But Shyam earns a total profit of 367000.
Let total profit earned by them be Rs. 400000 + x.
Hence, Shyam received 367000 – 256000 = Rs. 110000 from Rs. x profit.
i.e. Rs. 110000 is 74% of x.
Hence, x = 110000/0.74 = 150000
Hence, total profit earned by them = 400000 + 150000 = Rs. 550000
Hence, option (d).