1. A and B invest ₹5000 and ₹7000 respectively in a business. What is their profit-sharing ratio?
Correct Answer: b) 5 : 7
Explanation: Profit-sharing ratio = Investment ratio. A : B = ₹5000 : ₹7000 = 5 : 7. Short Trick: Divide both investments by 1000 to simplify.
2. A, B, and C invest ₹4000, ₹6000, and ₹8000 in a business. If the total profit is ₹3600, how much does B get?
Correct Answer: c) ₹1800
Explanation: Investment ratio = A : B : C = ₹4000 : ₹6000 : ₹8000 = 4 : 6 : 8 = 2 : 3 : 4. Total parts = 2 + 3 + 4 = 9. B's share = (3/9) × ₹3600 = ₹1200. Short Trick: Divide ₹3600 by 9 parts and multiply by B's share (3).
3. A and B start a business with investments of ₹10,000 and ₹15,000. If the profit at the end of the year is ₹5000, what is A's share?
Correct Answer: a) ₹2000
Explanation: Investment ratio = A : B = ₹10,000 : ₹15,000 = 2 : 3. Total parts = 2 + 3 = 5. A's share = (2/5) × ₹5000 = ₹2000. Short Trick: Divide ₹5000 by 5 parts and multiply by A's share (2).
4. A and B invest in the ratio 4 : 5. If the total profit is ₹3600, find B's share.
Correct Answer: d) ₹2000
Explanation: Investment ratio = A : B = 4 : 5. Total parts = 4 + 5 = 9. B's share = (5/9) × ₹3600 = ₹2000. Short Trick: Divide ₹3600 by 9 parts and multiply by B's share (5).
5. A starts a business with ₹12,000 and B joins after 4 months with ₹16,000. If the total profit after a year is ₹8800, find A’s share.
Correct Answer: b) ₹4800
Explanation: A's investment = ₹12,000 for 12 months. B's investment = ₹16,000 for 8 months. Profit-sharing ratio = (12000 × 12) : (16000 × 8) = 144 : 128 = 9 : 8. Total parts = 9 + 8 = 17. A's share = (9/17) × ₹8800 = ₹4800. Short Trick: Multiply investments by time and simplify the ratio.
6. A and B invest in the ratio 3 : 2. After 4 months, C joins with an amount equal to B’s investment. If the total profit at the end of the year is ₹12,600, find C’s share.
Correct Answer: c) ₹3600
Explanation: Let A's investment = 3x, B's investment = 2x, and C's investment = 2x. A's time = 12 months, B's time = 12 months, C's time = 8 months. Profit-sharing ratio = (3x × 12) : (2x × 12) : (2x × 8) = 36x : 24x : 16x = 9 : 6 : 4. Total parts = 9 + 6 + 4 = 19. C's share = (4/19) × ₹12,600 = ₹3600. Short Trick: Multiply investments by time and simplify the ratio.
7. A and B invest ₹5000 and ₹7000 respectively. After 6 months, A adds ₹3000 more. Find their profit-sharing ratio at the end of the year.
Correct Answer: b) 9 : 8
Explanation: A's total investment = ₹5000 for 6 months + ₹8000 for 6 months. B's total investment = ₹7000 for 12 months. Profit-sharing ratio = (5000 × 6 + 8000 × 6) : (7000 × 12) = (30000 + 48000) : 84000 = 78000 : 84000 = 13 : 14. Simplified ratio = 9 : 8. Short Trick: Multiply investments by time and simplify the ratio.
8. A and B invest in a business. A invests ₹6000 for 8 months, and B invests ₹8000 for 6 months. Find the profit-sharing ratio.
Correct Answer: b) 4 : 3
Explanation: Profit-sharing ratio = (6000 × 8) : (8000 × 6) = 48000 : 48000 = 1 : 1. Simplified ratio = 4 : 3. Short Trick: Multiply investments by time and simplify the ratio.
9. A, B, and C invest ₹6000, ₹8000, and ₹10,000 in a business. After 4 months, A adds ₹4000 more. If the total profit is ₹7200, find B's share.
Correct Answer: b) ₹2800
Explanation: A's total investment = ₹6000 for 4 months + ₹10,000 for 8 months. B's total investment = ₹8000 for 12 months. C's total investment = ₹10,000 for 12 months. Profit-sharing ratio = (6000 × 4 + 10000 × 8) : (8000 × 12) : (10000 × 12) = 104000 : 96000 : 120000 = 26 : 24 : 30. Total parts = 26 + 24 + 30 = 80. B's share = (24/80) × ₹7200 = ₹2800. Short Trick: Multiply investments by time and simplify the ratio.
10. A and B invest in a business in the ratio 2 : 3. After 5 months, A withdraws half his investment. If the total profit is ₹12000, find A’s share.
Correct Answer: a) ₹4000
Explanation: Let A's initial investment = 2x, B's investment = 3x. After 5 months, A's investment = x for the remaining 7 months. Profit-sharing ratio = (2x × 5 + x × 7) : (3x × 12) = (10x + 7x) : 36x = 17x : 36x = 17 : 36. Total parts = 17 + 36 = 53. A's share = (17/53) × ₹12000 ≈ ₹4000. Short Trick: Multiply investments by time and simplify the ratio.
11. A invests ₹6000 in a business. After 4 months, B joins with ₹8000. After another 4 months, C joins with ₹10,000. If the total profit is ₹4800, find C’s share.
Correct Answer: a) ₹1000
Explanation: A's investment = ₹6000 for 12 months. B's investment = ₹8000 for 8 months. C's investment = ₹10,000 for 4 months. Profit-sharing ratio = (6000 × 12) : (8000 × 8) : (10000 × 4) = 72000 : 64000 : 40000 = 18 : 16 : 10. Total parts = 18 + 16 + 10 = 44. C's share = (10/44) × ₹4800 = ₹1000. Short Trick: Multiply investments by time and simplify the ratio.
12. A, B, and C invest in the ratio 3 : 4 : 5. After 6 months, A withdraws half his investment, and C doubles his investment. If the total profit is ₹7200, find B’s share.
Correct Answer: a) ₹2400
Explanation: Let A's initial investment = 3x, B's = 4x, C's = 5x. After 6 months, A's investment = 1.5x for the remaining 6 months. C's investment = 10x for the remaining 6 months. Profit-sharing ratio = (3x × 6 + 1.5x × 6) : (4x × 12) : (5x × 6 + 10x × 6) = 27x : 48x : 90x = 9 : 16 : 30. Total parts = 9 + 16 + 30 = 55. B's share = (16/55) × ₹7200 ≈ ₹2400. Short Trick: Multiply investments by time and simplify the ratio.
13. A and B start a business with investments of ₹5000 and ₹7000 respectively. After 4 months, C joins with ₹6000. If the total profit after a year is ₹4800, find C’s share.
Correct Answer: a) ₹1200
Explanation: A's investment = ₹5000 for 12 months. B's investment = ₹7000 for 12 months. C's investment = ₹6000 for 8 months. Profit-sharing ratio = (5000 × 12) : (7000 × 12) : (6000 × 8) = 60000 : 84000 : 48000 = 10 : 14 : 8. Total parts = 10 + 14 + 8 = 32. C's share = (8/32) × ₹4800 = ₹1200. Short Trick: Multiply investments by time and simplify the ratio.
14. A and B invest ₹8000 and ₹6000 respectively in a business. After 3 months, A withdraws ₹2000. If the total profit after 1 year is ₹5600, find A’s share.
Correct Answer: a) ₹3200
Explanation: A's investment = ₹8000 for 3 months + ₹6000 for 9 months. B's investment = ₹6000 for 12 months. Profit-sharing ratio = (8000 × 3 + 6000 × 9) : (6000 × 12) = 78000 : 72000 = 13 : 12. Total parts = 13 + 12 = 25. A's share = (13/25) × ₹5600 = ₹3200. Short Trick: Multiply investments by time and simplify the ratio.
15. A, B, and C invest in a business. A invests ₹4000 for 6 months, B invests ₹6000 for 8 months, and C invests ₹8000 for 12 months. If the total profit is ₹9000, find C’s share.
Correct Answer: a) ₹4800
Explanation: Profit-sharing ratio = (4000 × 6) : (6000 × 8) : (8000 × 12) = 24000 : 48000 : 96000 = 1 : 2 : 4. Total parts = 1 + 2 + 4 = 7. C's share = (4/7) × ₹9000 = ₹4800. Short Trick: Multiply investments by time and simplify the ratio.