What are some CAT Partnership Practice Questions?
Q1. A, B and C started a business by investing ₹ 120000, ₹ 135000 and ₹ 150000 respectively. Find the share of each, out of an annual profit of ₹ 56700.
Answer: the share of A out of the annual profit of ₹56,700 is ₹16,800, the share of B is ₹18,900, and the share of C is ₹21,000.
Solution: Let the total investment be T.
A's investment : B's investment : C's investment = 120,000 : 135,000 : 150,000 = 12 : 13.5 : 15
A's share of profit = (12/40.5) × ₹56,700 = ₹16,800
B's share of profit = (13.5/40.5) × ₹56,700 = ₹18,900
C's share of profit = (15/40.5) × ₹56,700 = ₹21,000
Q2. Alfred started a business investing ₹ 45000. After 3 months, Peter joined him with a capital of ₹ 60000. After another 6 months, Ronald joined them with a capital of ₹ 90000. At the end of the year, they made a profit of ₹ 16500. Find the share of each.
Answer: the share of Alfred, Peter, and Ronald out of the annual profit of ₹16,500 is ₹5,500 each.
Solution: Let the total effective investment be T.
Alfred's effective investment : Peter's effective investment : Ronald's effective investment = 45,000 : 45,000 : 45,000 = 1 : 1 : 1
Alfred's share of profit = (1/3) × ₹16,500 = ₹5,500
Peter's share of profit = (1/3) × ₹16,500 = ₹5,500
Ronald's share of profit = (1/3) × ₹16,500 = ₹5,500
Q3. A, B and C start a business each investing ₹ 20000. After 5 months A withdrew ₹ 5000, B withdrew ₹ 4000 and C invests ₹ 6000 more. At the end of the year, a total profit of ₹ 69900 was recorded. Find the share of each.
Answer: the share of A out of the annual profit of ₹69,900 is ₹20,499.60, the share of B is ₹21,200.40, and the share of C is ₹28,200.
Solution: Let the total effective investment be T.
A's effective investment : B's effective investment : C's effective investment = 17.083 : 17.667 : 23.5
A's share of profit = (17.083/58.25) × ₹69,900 = ₹20,499.60
B's share of profit = (17.667/58.25) × ₹69,900 = ₹21,200.40
C's share of profit = (23.5/58.25) × ₹69,900 = ₹28,200
Q4. A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two-thirds of what C invests. At the end of the year, the profit earned is ₹ 6600. What is the share of B?
Answer: the share of B out of the annual profit of ₹6,600 is ₹1,200.
Solution: Let the total investment be T.
A's investment : B's investment : C's investment = 6 : 2 : 3
B's share of profit = (2/11) × ₹6,600 = ₹1,200
What are the must-do Partnership questions for the CAT exam?
Q5. A, B and C enter into partnership with capitals of ₹ 25000, ₹ 30000 and ₹ 15000 respectively. A is the
working partner and he gets 30% of the profit for managing the business. The balance profit is distributed
in proportion to the capital investment. At the year-end, A gets ₹ 200 more than B and C together. Find
the total profit and the share of each.
Answer: the total profit is ₹2,000, and the share of A is ₹1,100, the share of B is ₹600, and the share of C is ₹300.
Solution: Let the total profit be P.
A's share = 0.3P + (25,000 / 70,000) × 0.7P = 0.55P
B's share = (30,000 / 70,000) × 0.7P
C's share = (15,000 / 70,000) × 0.7P
A's share - (B's share + C's share) = 200
0.55P - 0.45P = 200
P = ₹2,000
A's share = 0.55 × ₹2,000 = ₹1,100
B's share = (30,000 / 70,000) × 0.7 × ₹2,000 = ₹600
C's share = (15,000 / 70,000) × 0.7 × ₹2,000 = ₹300
Q6. Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is ₹ 720, find the total rent of the field.
Answer: the total rent of the field is ₹3,240.
Solution: Let the total rent be R.
A's grazing units : B's grazing units : C's grazing units : D's grazing units = 18 : 12.5 : 35 : 15.75
A's share of rent = (18/81.25) × R = ₹720
R = (₹720 × 81.25) / 18
R = ₹3,240
B's share of rent = (12.5/81.25) × ₹3,240 = ₹500
C's share of rent = (35/81.25) × ₹3,240 = ₹1,400
D's share of rent = (15.75/81.25) × ₹3,240 = ₹620
Q7. A, B and C took a house on rent for one year for ₹ 13824. They remained together for 4 months and then C left the house. After 5 more months, B also left the house. How much rent should each pay?
Answer: A should pay ₹6,144, B should pay ₹6,144, and C should pay ₹1,536 as their share of the rent.
Solution: Let the total rent be R = ₹13,824.
Rent for the first 4 months = (4/12) × R = ₹4,608
Each person's share for the first 4 months = ₹4,608 / 3 = ₹1,536
Rent for the remaining 8 months = (8/12) × R = ₹9,216
A's share for the remaining 8 months = B's share for the remaining 8 months = ₹9,216 / 2 = ₹4,608
A's total rent = ₹1,536 + ₹4,608 = ₹6,144
B's total rent = ₹1,536 + ₹4,608 = ₹6,144
C's total rent = ₹1,536
Q8. A invested ₹ 76000 in a business. After few months, B joined him with ₹ 57000. At the end of the year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join?
Answer: B joined the business 4 months after A.
Solution: Let B join the business x months after A.
A's effective investment = ₹76,000 × 1
B's effective investment = ₹57,000 × (12 - x)/12
Ratio of their effective investments = 76 : [57 × (1 - x/12)]
Since the total profit was divided in the ratio 2:1, their effective investments should be in the ratio 2:1.
76 : [57 × (1 - x/12)] = 2 : 1
76 / [57 × (1 - x/12)] = 2
(76 × 12) / [57 × (12 - x)] = 2
912 / (684 - 57x) = 2
456 = 684 - 57x
57x = 228
x = 4
What were the previous year's CAT Partnership questions?
Q9. The ratio of investments of two partners A and B is 11 : 12 and the ratio of their profits is 2 : 3. If A invested the money for 8 months, then for how much time B invested his money?
Answer: B invested the money for 12 months.
Solution: Let B invest the money for x months.
A's effective investment = 11 × 8/12
B's effective investment = 12 × x/12
Ratio of their effective investments = (11 × 8/12) : (12 × x/12)
Ratio of their effective investments = 88/12 : x
Since the total profit is divided in the ratio 2:3, their effective investments should be in the ratio 2:3.
(88/12) : x = 2 : 3
(88/12) / x = 2/3
88/12x = 2/3
88 = 18x
x = 88/18
x = 12
Q10. A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another ₹ 270000 and C, at the end of 2 years, also invests ₹ 270000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of each.
Answer: the initial investments of A, B, and C were ₹720,000, ₹480,000, and ₹960,000, respectively.
Solution: Let A's initial investment = 3x
B's initial investment = 2x
C's initial investment = 4x
After one year, B invests an additional ₹270,000.
B's effective investment = 2x + ₹270,000
After two years, C invests an additional ₹270,000.
C's effective investment = 4x + ₹270,000
At the end of three years, profits are shared in the ratio of 3:4:5.
A's effective investment : B's effective investment : C's effective investment = 3 : 4 : 5
3x : (2x + ₹270,000) : (4x + ₹270,000) = 3 : 4 : 5
Cross-multiplying the first ratio:
3x / (2x + ₹270,000) = 3/4
9x = 8x + 2,160,000
x = ₹240,000
Substituting x = ₹240,000 in the initial investments:
A's initial investment = 3x = 3 × ₹240,000 = ₹720,000
B's initial investment = 2x = 2 × ₹240,000 = ₹480,000
C's initial investment = 4x = 4 × ₹240,000 = ₹960,000
Q11. A, B and C enter into a partnership. Their capital contribution is in the ratio 21 : 18 : 14. At the end of the business term they share profits in the ratio 15 : 8 : 9. Find the ratio of time for which they invest their capitals.
Answer: the ratio of the time periods for which A, B, and C invested their capitals is x:y:z = k:3.11k:4.5k = 1:3.11:4.5.
Solution: Let A invest for x months, B invest for y months, and C invest for z months.
A's effective investment = 21x
B's effective investment = 18y
C's effective investment = 14z
Since their capital contributions are in the ratio of 21:18:14, their effective investments should be in the same ratio.
21x : 18y : 14z = 21 : 18 : 14
3x : 2.57y : 2z = 3 : 2.57 : 2
Since they share the profits in the ratio of 15:8:9, their effective investments should be in the same ratio.
3x : 2.57y : 2z = 15 : 8 : 9
From the first equation:
3x = 3k (let 3k represent the common factor)
x = k
From the second equation:
2.57y = 8k
y = 8k / 2.57
y = 3.11k
From the second equation:
2z = 9k
z = 9k / 2
z = 4.5k
Q12. In a partnership, the ratio of investments by partners P and Q is 3 : 5. If the ratio of their profits is 4 : 7, and partner P invested his money for 9 months, for how long did partner Q invest his money?
Answer: partner Q invested his money for 3.75 × 12 = 45 months or 3 years and 9 months.
Solution: Let partner Q invest his money for x months.
P's effective investment = 3 × (9/12)
Q's effective investment = 5 × (x/12)
Ratio of their effective investments = [3 × (9/12)] : [5 × (x/12)]
Ratio of their effective investments = 27/12 : (5x/12)
Ratio of their effective investments = 27 : 5x
Since the total profit is divided in the ratio 4:7, their effective investments should be in the same ratio.
27 : 5x = 4 : 7
27/5x = 4/7
135 = 28x
x = 135/28
x = 15/4
x = 3.75
What were the Partnership questions on the CAT 2022 exam?
Q13. D, E, and F started a venture by investing ₹ 180000, ₹ 210000, and ₹ 240000 respectively. Calculate their respective shares out of an annual profit of ₹ 84000.
Answer: the share of D out of the annual profit of ₹84,000 is ₹24,000, the share of E is ₹28,000, and the share of F is ₹32,000.
Solution: Let the total investment be T.
D's investment : E's investment : F's investment = 9 : 10.5 : 12
D's share of profit = (9/31.5) × ₹84,000 = ₹24,000
E's share of profit = (10.5/31.5) × ₹84,000 = ₹28,000
F's share of profit = (12/31.5) × ₹84,000 = ₹32,000
Q14. D, E, and F rented a workshop for one year for ₹ 18000. They stayed together for 6 months, after which D left. E stayed for 3 more months before leaving, while F stayed for the entire year. How much rent should each person pay?
Answer: D should pay ₹3,000, E should pay ₹5,250, and F should pay ₹9,750 as their share of the rent.
Solution: Let the total rent be R = ₹18,000.
Rent for the first 6 months = (6/12) × R = ₹9,000
Each person's share for the first 6 months = ₹9,000 / 3 = ₹3,000
Rent for the next 3 months = (3/12) × R = ₹4,500
E's share for the next 3 months = F's share for the next 3 months = ₹4,500 / 2 = ₹2,250
Rent for the remaining 3 months = (3/12) × R = ₹4,500
F's share for the remaining 3 months = ₹4,500
D's total rent = ₹3,000
E's total rent = ₹3,000 + ₹2,250 = ₹5,250
F's total rent = ₹3,000 + ₹2,250 + ₹4,500 = ₹9,750
Q15. Emily started a bakery business by investing ₹ 60000. After 2 months, Sarah joined her with a capital of ₹ 80000. After another 4 months, Michael joined them with a capital of ₹ 120000. At the end of the year, they made a profit of ₹ 24000. Find the share of each partner.
Answer: the share of Emily out of the annual profit of ₹24,000 is ₹7,710.15, the share of Sarah is ₹8,573.69, and the share of Michael is ₹7,710.15.
Solution: Let the total profit be P = ₹24,000.
Emily's effective investment : Sarah's effective investment : Michael's effective investment = 5 : 5.56 : 5
Emily's share = (5/15.56) × P = ₹7,710.15
Sarah's share = (5.56/15.56) × P = ₹8,573.69
Michael's share = (5/15.56) × P = ₹7,710.15
Q16. X, Y, and Z decide to start a tech startup together. X invests 4 times as much as Y invests, and Y invests half of what Z invests. At the end of the year, they earn a profit of ₹ 48000. What is the share of Y?
Answer: the share of Y out of the annual profit of ₹48,000 is ₹6,857.14.
Solution: Let Y's investment be x.
X's investment = 4x
Z's investment = 2x
X's investment : Y's investment : Z's investment = 8 : 2 : 4
Let the shares of X, Y, and Z be represented by x, y, and z, respectively.
x : y : z = 8 : 2 : 4
x + y + z = ₹48,000
Substituting the ratios, we get:
8k + 2k + 4k = ₹48,000
14k = ₹48,000
k = ₹48,000 / 14
k = ₹3,428.57
Y's share = y = 2k = 2 × ₹3,428.57 = ₹6,857.14
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