SSC CGL (Prelims) General: Partnership questions with solutions

Q1. Two men, M and N, rent a pasture. M uses 12 cows for 4 months and 18 goats for 5 months, while N uses 26 goats for 7 months. If 3 cows are equivalent to 7 goats, what is M's share of the rent?

1. 101/192
2. 110/192
3. 105/192
4. 60/192

Answer: 101/192

Since 3 cows = 7 goats, 1 cow = 7/3 goats. M's usage = 12 cows for 4 months + 18 goats for 5 months = 12×4×7/3 + 18×5 = 112 + 90 = 202 goat-month units. N's usage = 26×7 = 182 goat-month units. So M's share = 202/(202+182) = 202/384 = 101/192.

Q2. P, Q, and R started a business with capitals in the ratio 1:2:4. After 4 months, R withdrew 50% of his capital. After another 2 months, Q withdrew 25% of his capital. The business continued for 12 months in total. If the total profit is ₹2,40,000, find the profit ratio P:Q:R.

1. 32: 21: 12
2. 21: 12: 33
3. 12: 21: 32
4. 12: 33: 42

Answer: 12: 21: 32

In partnership problems, profit is proportional to capital × time. Compute the effective investments of P, Q, and R over 12 months, considering the withdrawals, and then reduce the ratio to simplest form. This gives the profit-sharing ratio as 12:21:32.

Q3. Two partners, M and N, share a grazing field. M grazes 12 cows for 4 months and 18 goats for 5 months; N grazes 26 goats for 7 months. Given that 3 cows graze as much as 7 goats, what fraction of the total rent should M pay?

1. 101/192
2. 110/192
3. 105/192
4. 60/192

Answer: 101/192

Since 3 cows = 7 goats, 1 cow = 7/3 goats. Convert M’s cows into goat-equivalents and multiply by months, then add the goat contribution. Do the same for N, and take M’s contribution divided by the total contribution to get the rent fraction.

Q4. X and Y begin a venture investing Rs 60,000 and Rs 90,000 respectively. After 6 months, X doubles his investment while Y withdraws Rs 30,000. If the year's total profit is Rs 62,000, find Y's share, rounded to the nearest rupee.

1. Rs 28,182
2. Rs 30,105
3. Rs 33,000
4. Rs 35,512

Answer: Rs 28,182

Profit is shared in the ratio of capital-time products. X’s contribution is 60,000×6 + 120,000×6, while Y’s is 90,000×6 + 60,000×6. Using this ratio, Y’s share of the total profit comes out to Rs 28,182 approximately.