This lesson gives one rule, the reason it works and seven worked examples. It also lists the traps that cost marks.
Read the Article: Partnership: Formulas, Shortcuts and Solved Examples →
0 / 25 correct · click an option to check it
Q1. Meera started a business investing Rs. 21000. After 3 months, Rajesh joined with a capital of Rs. 25000. At the end of the year, they made a profit of Rs. 2120. What is Rajesh’s share?
Show answer and explanation
Answer: B
Let Meera invest Rs. 21000 for the full year, so Meera’s time = 12 months. Rajesh joined after 3 months, investing Rs. 25000. So Rajesh’s time = 12 – 3 = 9 months. Meera’s equivalent capital = 21000 x 12 = 252000. Rajesh’s equivalent capital = 25000 x 9 = 225000. Ratio of equivalent capitals = 252000:225000, which simplifies to 28:25. Rajesh’s share = 25/53 x Rs. 2120 = Rs. 1000. Check: Meera’s share = 28/53 x Rs. 2120 = Rs. 1120. Rs. 1120 plus Rs. 1000 equals Rs. 2120, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q2. Meera started a business investing Rs. 42000. After 3 months, Rajesh joined with a capital of Rs. 18000. At the end of the year, they made a profit of Rs. 1480. What is Rajesh’s share?
Show answer and explanation
Answer: B
Let Meera invest Rs. 42000 for the full year, so Meera’s time = 12 months. Rajesh joined after 3 months, investing Rs. 18000. So Rajesh’s time = 12 – 3 = 9 months. Meera’s equivalent capital = 42000 x 12 = 504000. Rajesh’s equivalent capital = 18000 x 9 = 162000. Ratio of equivalent capitals = 504000:162000, which simplifies to 28:9. Rajesh’s share = 9/37 x Rs. 1480 = Rs. 360. Check: Meera’s share = 28/37 x Rs. 1480 = Rs. 1120. Rs. 1120 plus Rs. 360 equals Rs. 1480, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q3. Meera started a business investing Rs. 32000. After 2 months, Rajesh joined with a capital of Rs. 6000. At the end of the year, they made a profit of Rs. 1258. What is Rajesh’s share?
Show answer and explanation
Answer: D
Let Meera invest Rs. 32000 for the full year, so Meera’s time = 12 months. Rajesh joined after 2 months, investing Rs. 6000. So Rajesh’s time = 12 – 2 = 10 months. Meera’s equivalent capital = 32000 x 12 = 384000. Rajesh’s equivalent capital = 6000 x 10 = 60000. Ratio of equivalent capitals = 384000:60000, which simplifies to 32:5. Rajesh’s share = 5/37 x Rs. 1258 = Rs. 170. Check: Meera’s share = 32/37 x Rs. 1258 = Rs. 1088. Rs. 1088 plus Rs. 170 equals Rs. 1258, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q4. Meera started a business investing Rs. 22000. After 5 months, Rajesh joined with a capital of Rs. 31000. At the end of the year, they made a profit of Rs. 10101. What is Rajesh’s share?
Show answer and explanation
Answer: C
Let Meera invest Rs. 22000 for the full year, so Meera’s time = 12 months. Rajesh joined after 5 months, investing Rs. 31000. So Rajesh’s time = 12 – 5 = 7 months. Meera’s equivalent capital = 22000 x 12 = 264000. Rajesh’s equivalent capital = 31000 x 7 = 217000. Ratio of equivalent capitals = 264000:217000, which simplifies to 264:217. Rajesh’s share = 217/481 x Rs. 10101 = Rs. 4557. Check: Meera’s share = 264/481 x Rs. 10101 = Rs. 5544. Rs. 5544 plus Rs. 4557 equals Rs. 10101, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q5. Meera started a business investing Rs. 12000. After 2 months, Rajesh joined with a capital of Rs. 9000. At the end of the year, they made a profit of Rs. 234. What is Rajesh’s share?
Show answer and explanation
Answer: A
Let Meera invest Rs. 12000 for the full year, so Meera’s time = 12 months. Rajesh joined after 2 months, investing Rs. 9000. So Rajesh’s time = 12 – 2 = 10 months. Meera’s equivalent capital = 12000 x 12 = 144000. Rajesh’s equivalent capital = 9000 x 10 = 90000. Ratio of equivalent capitals = 144000:90000, which simplifies to 8:5. Rajesh’s share = 5/13 x Rs. 234 = Rs. 90. Check: Meera’s share = 8/13 x Rs. 234 = Rs. 144. Rs. 144 plus Rs. 90 equals Rs. 234, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q6. Meera started a business investing Rs. 32000. After 4 months, Rajesh joined with a capital of Rs. 7000. At the end of the year, they made a profit of Rs. 440. What is Rajesh’s share?
Show answer and explanation
Answer: C
Let Meera invest Rs. 32000 for the full year, so Meera’s time = 12 months. Rajesh joined after 4 months, investing Rs. 7000. So Rajesh’s time = 12 – 4 = 8 months. Meera’s equivalent capital = 32000 x 12 = 384000. Rajesh’s equivalent capital = 7000 x 8 = 56000. Ratio of equivalent capitals = 384000:56000, which simplifies to 48:7. Rajesh’s share = 7/55 x Rs. 440 = Rs. 56. Check: Meera’s share = 48/55 x Rs. 440 = Rs. 384. Rs. 384 plus Rs. 56 equals Rs. 440, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q7. Meera started a business investing Rs. 21000. After 4 months, Rajesh joined with a capital of Rs. 41000. At the end of the year, they made a profit of Rs. 1015. What is Rajesh’s share?
Show answer and explanation
Answer: D
Let Meera invest Rs. 21000 for the full year, so Meera’s time = 12 months. Rajesh joined after 4 months, investing Rs. 41000. So Rajesh’s time = 12 – 4 = 8 months. Meera’s equivalent capital = 21000 x 12 = 252000. Rajesh’s equivalent capital = 41000 x 8 = 328000. Ratio of equivalent capitals = 252000:328000, which simplifies to 63:82. Rajesh’s share = 82/145 x Rs. 1015 = Rs. 574. Check: Meera’s share = 63/145 x Rs. 1015 = Rs. 441. Rs. 441 plus Rs. 574 equals Rs. 1015, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q8. Meera started a business investing Rs. 23000. After 8 months, Rajesh joined with a capital of Rs. 42000. At the end of the year, they made a profit of Rs. 703. What is Rajesh’s share?
Show answer and explanation
Answer: A
Let Meera invest Rs. 23000 for the full year, so Meera’s time = 12 months. Rajesh joined after 8 months, investing Rs. 42000. So Rajesh’s time = 12 – 8 = 4 months. Meera’s equivalent capital = 23000 x 12 = 276000. Rajesh’s equivalent capital = 42000 x 4 = 168000. Ratio of equivalent capitals = 276000:168000, which simplifies to 23:14. Rajesh’s share = 14/37 x Rs. 703 = Rs. 266. Check: Meera’s share = 23/37 x Rs. 703 = Rs. 437. Rs. 437 plus Rs. 266 equals Rs. 703, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q9. Meera started a business investing Rs. 7000. After 8 months, Rajesh joined with a capital of Rs. 29000. At the end of the year, they made a profit of Rs. 250. What is Rajesh’s share?
Show answer and explanation
Answer: B
Let Meera invest Rs. 7000 for the full year, so Meera’s time = 12 months. Rajesh joined after 8 months, investing Rs. 29000. So Rajesh’s time = 12 – 8 = 4 months. Meera’s equivalent capital = 7000 x 12 = 84000. Rajesh’s equivalent capital = 29000 x 4 = 116000. Ratio of equivalent capitals = 84000:116000, which simplifies to 21:29. Rajesh’s share = 29/50 x Rs. 250 = Rs. 145. Check: Meera’s share = 21/50 x Rs. 250 = Rs. 105. Rs. 105 plus Rs. 145 equals Rs. 250, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q10. Meera started a business investing Rs. 22000. After 2 months, Rajesh joined with a capital of Rs. 11000. At the end of the year, they made a profit of Rs. 476. What is Rajesh’s share?
Show answer and explanation
Answer: D
Let Meera invest Rs. 22000 for the full year, so Meera’s time = 12 months. Rajesh joined after 2 months, investing Rs. 11000. So Rajesh’s time = 12 – 2 = 10 months. Meera’s equivalent capital = 22000 x 12 = 264000. Rajesh’s equivalent capital = 11000 x 10 = 110000. Ratio of equivalent capitals = 264000:110000, which simplifies to 12:5. Rajesh’s share = 5/17 x Rs. 476 = Rs. 140. Check: Meera’s share = 12/17 x Rs. 476 = Rs. 336. Rs. 336 plus Rs. 140 equals Rs. 476, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q11. Meera started a business investing Rs. 5000. After 8 months, Rajesh joined with a capital of Rs. 22000. At the end of the year, they made a profit of Rs. 148. What is Rajesh’s share?
Show answer and explanation
Answer: A
Let Meera invest Rs. 5000 for the full year, so Meera’s time = 12 months. Rajesh joined after 8 months, investing Rs. 22000. So Rajesh’s time = 12 – 8 = 4 months. Meera’s equivalent capital = 5000 x 12 = 60000. Rajesh’s equivalent capital = 22000 x 4 = 88000. Ratio of equivalent capitals = 60000:88000, which simplifies to 15:22. Rajesh’s share = 22/37 x Rs. 148 = Rs. 88. Check: Meera’s share = 15/37 x Rs. 148 = Rs. 60. Rs. 60 plus Rs. 88 equals Rs. 148, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q12. Meera started a business investing Rs. 17000. After 7 months, Rajesh joined with a capital of Rs. 12000. At the end of the year, they made a profit of Rs. 110. What is Rajesh’s share?
Show answer and explanation
Answer: B
Let Meera invest Rs. 17000 for the full year, so Meera’s time = 12 months. Rajesh joined after 7 months, investing Rs. 12000. So Rajesh’s time = 12 – 7 = 5 months. Meera’s equivalent capital = 17000 x 12 = 204000. Rajesh’s equivalent capital = 12000 x 5 = 60000. Ratio of equivalent capitals = 204000:60000, which simplifies to 17:5. Rajesh’s share = 5/22 x Rs. 110 = Rs. 25. Check: Meera’s share = 17/22 x Rs. 110 = Rs. 85. Rs. 85 plus Rs. 25 equals Rs. 110, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q13. Meera started a business investing Rs. 42000. After 8 months, Rajesh joined with a capital of Rs. 40000. At the end of the year, they made a profit of Rs. 2324. What is Rajesh’s share?
Show answer and explanation
Answer: C
Let Meera invest Rs. 42000 for the full year, so Meera’s time = 12 months. Rajesh joined after 8 months, investing Rs. 40000. So Rajesh’s time = 12 – 8 = 4 months. Meera’s equivalent capital = 42000 x 12 = 504000. Rajesh’s equivalent capital = 40000 x 4 = 160000. Ratio of equivalent capitals = 504000:160000, which simplifies to 63:20. Rajesh’s share = 20/83 x Rs. 2324 = Rs. 560. Check: Meera’s share = 63/83 x Rs. 2324 = Rs. 1764. Rs. 1764 plus Rs. 560 equals Rs. 2324, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q14. Vijay invests Rs. 7000 for 8 months, and Ashok invests Rs. 38000 for 4 months in a business. Out of a total profit of Rs. 312, what is Vijay’s share?
Show answer and explanation
Answer: D
Let Vijay’s capital = Rs. 7000 for 8 months, and Ashok’s capital = Rs. 38000 for 4 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 7000 x 8 = 56000. Ashok’s equivalent capital = 38000 x 4 = 152000. Ratio of equivalent capitals = 56000:152000, which simplifies to 7:19. Vijay’s share = 7/26 x Rs. 312 = Rs. 84. Check: Ashok’s share = 19/26 x Rs. 312 = Rs. 228. Rs. 84 plus Rs. 228 equals Rs. 312, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q15. Vijay invests Rs. 21000 for 12 months, and Ashok invests Rs. 30000 for 7 months in a business. Out of a total profit of Rs. 242, what is Vijay’s share?
Show answer and explanation
Answer: C
Let Vijay’s capital = Rs. 21000 for 12 months, and Ashok’s capital = Rs. 30000 for 7 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 21000 x 12 = 252000. Ashok’s equivalent capital = 30000 x 7 = 210000. Ratio of equivalent capitals = 252000:210000, which simplifies to 6:5. Vijay’s share = 6/11 x Rs. 242 = Rs. 132. Check: Ashok’s share = 5/11 x Rs. 242 = Rs. 110. Rs. 132 plus Rs. 110 equals Rs. 242, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q16. Vijay invests Rs. 28000 for 10 months, and Ashok invests Rs. 21000 for 6 months in a business. Out of a total profit of Rs. 435, what is Vijay’s share?
Show answer and explanation
Answer: A
Let Vijay’s capital = Rs. 28000 for 10 months, and Ashok’s capital = Rs. 21000 for 6 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 28000 x 10 = 280000. Ashok’s equivalent capital = 21000 x 6 = 126000. Ratio of equivalent capitals = 280000:126000, which simplifies to 20:9. Vijay’s share = 20/29 x Rs. 435 = Rs. 300. Check: Ashok’s share = 9/29 x Rs. 435 = Rs. 135. Rs. 300 plus Rs. 135 equals Rs. 435, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q17. Vijay invests Rs. 36000 for 5 months, and Ashok invests Rs. 23000 for 5 months in a business. Out of a total profit of Rs. 1534, what is Vijay’s share?
Show answer and explanation
Answer: B
Let Vijay’s capital = Rs. 36000 for 5 months, and Ashok’s capital = Rs. 23000 for 5 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 36000 x 5 = 180000. Ashok’s equivalent capital = 23000 x 5 = 115000. Ratio of equivalent capitals = 180000:115000, which simplifies to 36:23. Vijay’s share = 36/59 x Rs. 1534 = Rs. 936. Check: Ashok’s share = 23/59 x Rs. 1534 = Rs. 598. Rs. 936 plus Rs. 598 equals Rs. 1534, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q18. Vijay invests Rs. 54000 for 11 months, and Ashok invests Rs. 6000 for 3 months in a business. Out of a total profit of Rs. 1122, what is Vijay’s share?
Show answer and explanation
Answer: B
Let Vijay’s capital = Rs. 54000 for 11 months, and Ashok’s capital = Rs. 6000 for 3 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 54000 x 11 = 594000. Ashok’s equivalent capital = 6000 x 3 = 18000. Ratio of equivalent capitals = 594000:18000, which simplifies to 33:1. Vijay’s share = 33/34 x Rs. 1122 = Rs. 1089. Check: Ashok’s share = 1/34 x Rs. 1122 = Rs. 33. Rs. 1089 plus Rs. 33 equals Rs. 1122, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q19. Vijay invests Rs. 14000 for 9 months, and Ashok invests Rs. 52000 for 3 months in a business. Out of a total profit of Rs. 470, what is Vijay’s share?
Show answer and explanation
Answer: A
Let Vijay’s capital = Rs. 14000 for 9 months, and Ashok’s capital = Rs. 52000 for 3 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 14000 x 9 = 126000. Ashok’s equivalent capital = 52000 x 3 = 156000. Ratio of equivalent capitals = 126000:156000, which simplifies to 21:26. Vijay’s share = 21/47 x Rs. 470 = Rs. 210. Check: Ashok’s share = 26/47 x Rs. 470 = Rs. 260. Rs. 210 plus Rs. 260 equals Rs. 470, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q20. Vijay invests Rs. 42000 for 2 months, and Ashok invests Rs. 23000 for 6 months in a business. Out of a total profit of Rs. 592, what is Vijay’s share?
Show answer and explanation
Answer: D
Let Vijay’s capital = Rs. 42000 for 2 months, and Ashok’s capital = Rs. 23000 for 6 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 42000 x 2 = 84000. Ashok’s equivalent capital = 23000 x 6 = 138000. Ratio of equivalent capitals = 84000:138000, which simplifies to 14:23. Vijay’s share = 14/37 x Rs. 592 = Rs. 224. Check: Ashok’s share = 23/37 x Rs. 592 = Rs. 368. Rs. 224 plus Rs. 368 equals Rs. 592, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q21. Vijay invests Rs. 46000 for 11 months, and Ashok invests Rs. 11000 for 2 months in a business. Out of a total profit of Rs. 576, what is Vijay’s share?
Show answer and explanation
Answer: C
Let Vijay’s capital = Rs. 46000 for 11 months, and Ashok’s capital = Rs. 11000 for 2 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 46000 x 11 = 506000. Ashok’s equivalent capital = 11000 x 2 = 22000. Ratio of equivalent capitals = 506000:22000, which simplifies to 23:1. Vijay’s share = 23/24 x Rs. 576 = Rs. 552. Check: Ashok’s share = 1/24 x Rs. 576 = Rs. 24. Rs. 552 plus Rs. 24 equals Rs. 576, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q22. Vijay invests Rs. 40000 for 5 months, and Ashok invests Rs. 7000 for 4 months in a business. Out of a total profit of Rs. 684, what is Vijay’s share?
Show answer and explanation
Answer: A
Let Vijay’s capital = Rs. 40000 for 5 months, and Ashok’s capital = Rs. 7000 for 4 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 40000 x 5 = 200000. Ashok’s equivalent capital = 7000 x 4 = 28000. Ratio of equivalent capitals = 200000:28000, which simplifies to 50:7. Vijay’s share = 50/57 x Rs. 684 = Rs. 600. Check: Ashok’s share = 7/57 x Rs. 684 = Rs. 84. Rs. 600 plus Rs. 84 equals Rs. 684, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q23. Vijay invests Rs. 8000 for 11 months, and Ashok invests Rs. 18000 for 12 months in a business. Out of a total profit of Rs. 38, what is Vijay’s share?
Show answer and explanation
Answer: C
Let Vijay’s capital = Rs. 8000 for 11 months, and Ashok’s capital = Rs. 18000 for 12 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 8000 x 11 = 88000. Ashok’s equivalent capital = 18000 x 12 = 216000. Ratio of equivalent capitals = 88000:216000, which simplifies to 11:27. Vijay’s share = 11/38 x Rs. 38 = Rs. 11. Check: Ashok’s share = 27/38 x Rs. 38 = Rs. 27. Rs. 11 plus Rs. 27 equals Rs. 38, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q24. Vijay invests Rs. 23000 for 4 months, and Ashok invests Rs. 59000 for 5 months in a business. Out of a total profit of Rs. 3483, what is Vijay’s share?
Show answer and explanation
Answer: D
Let Vijay’s capital = Rs. 23000 for 4 months, and Ashok’s capital = Rs. 59000 for 5 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 23000 x 4 = 92000. Ashok’s equivalent capital = 59000 x 5 = 295000. Ratio of equivalent capitals = 92000:295000, which simplifies to 92:295. Vijay’s share = 92/387 x Rs. 3483 = Rs. 828. Check: Ashok’s share = 295/387 x Rs. 3483 = Rs. 2655. Rs. 828 plus Rs. 2655 equals Rs. 3483, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples
Q25. Vijay invests Rs. 30000 for 5 months, and Ashok invests Rs. 44000 for 4 months in a business. Out of a total profit of Rs. 4401, what is Vijay’s share?
Show answer and explanation
Answer: B
Let Vijay’s capital = Rs. 30000 for 5 months, and Ashok’s capital = Rs. 44000 for 4 months. In a compound partnership, profit share depends on capital multiplied by time. Vijay’s equivalent capital = 30000 x 5 = 150000. Ashok’s equivalent capital = 44000 x 4 = 176000. Ratio of equivalent capitals = 150000:176000, which simplifies to 75:88. Vijay’s share = 75/163 x Rs. 4401 = Rs. 2025. Check: Ashok’s share = 88/163 x Rs. 4401 = Rs. 2376. Rs. 2025 plus Rs. 2376 equals Rs. 4401, the full profit.
Related topics: Partnership: Formulas, Shortcuts and Solved Examples