1.A, B and C invested capitals in the ratio 3 : 4 : 9; the timing of their investments being in the ratio 9 : 6 : 7. In what ratio would their profit be distributed?
(a) 9 : 8 : 21
(b) 27 : 25 : 63
(c) 27 : 24 : 36
(d) 9 : 8 : 12
1.(a)
2.A, B and C invest their capitals in a business. If the ratio of their periods of investments are 7 : 3 : 5 and their profits are in the ratio of 2 : 1 : 2. Find the ratio in which the investments are made by A, B and C.
(a) 30 : 35 : 42
(b) 7 : 6 : 10
(c) 42 : 30 : 35
(d) 42 : 25 : 35
2.(a)
3.A, B and C are partners. A receives 2/5 of the profit and B and C share the remaining profit equally. A’s income is increased by Rs. 220 when the profit rises from 8% to 10%. Find the capitals invested by A, B and C.
(a)8850
(b)8860
(c)8250
(d)8230
3.(c) Soln:
Detail Method: For A’s share: (10% – 8%) = Rs. 220
∴ 100% ≡220/2×100= Rs. 11000
∴ A’s capital ≡Rs. 11000
For B’s & share: 2/5≡ 11000
∴3/5≡11000/2×3≡ Rs. 16500
∴ B’s and C’s capitals are Rs. 8250 each.
Quicker Method: Applying the above rule, we have,
A’s capital = (100×220)/(10-8)= Rs. 11000
B’s and C’s capitals = ((100 × 220)/(10 - 8) × (1- 2/5))/2
= Rs. 8250 each.
4.A, B and C are partners. A receives 2/7 of the profit and B and C share the remaining profit equally. A’s income is increased by Rs. 240 when the profit rises from 10% to 15%. Find the capitals invested by B and C.
(a) Rs. 2400
(b) Rs. 1200
(c) Rs. 4800
(d) Rs. 6000
4.(d)
5.Two partners invest Rs. 125,000 and Rs. 85,000 respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs. 300 more than the other, find the total profit made in the business.
(a)3937.50
(b)3936.50
(c)3936.55
(d)3937.56
5.(a)
Soln: Detail Method: The difference counts only due to the 40% of the profit which was distributed according to their investments.
Let the total profit be Rs x.
Then 40% of x is distributed in the ratio 125,000 : 85,000 = 25 : 17
Therefore, the share of the first partner
=40% of x (25/(25+17))
=40% of x (25/42)=40x/100 (25/42)=5x/21
andthe share of the second partner
=40% of x (17/42)=17x/105
Now, from the question,
thedifference in share = 5x/21-17x/105=300
or,(x(25-17))/105=300
∴ x = (300×105)/8=Rs.3937.50
Quiker Mothod: Applying the above rule, we have,
Step I: The ratio of profit = 125,000 : 85,000 = 25 : 17
Step II: total profit = 300(100/40)((25+17)/(25-17))
= Rs. 3937.50
6.Two partners invest Rs. 24750 and Rs. 16500 respectively in a business and agree that 20% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets Rs. 400 more than the other, find the total profit made in the business.
(a) Rs. 5000
(b) Rs. 2500
(c) Rs. 3500
(d) Rs. 4500
6.(b)
7.A and B invested in the ratio 3 : 2 in a business. If 5% of the total profit goes to charity and A’s share is Rs. 855, find the total profit.
(a) 1600
(b) 1500
(c) 1400
(d) 1300
7.(b)
8.A and B invested in the ratio 5 : 3 in a business. If 10% of the total profit goes to charity and A’s share is Rs. 900, find the total profit.
(a) Rs. 1600
(b) Rs. 1400
(c) Rs. 1500
(d) Rs. 1800
8.(a)
Details Method: Suppose the total profit is Rs. 100.
Then Rs. 5 goes to charity.
Now, Rs. 95 is divided in the ratio 3 : 2.
A’s share = 95/(3+2)×3=Rs.57
But we see that A’s actual share is Rs. 855.
Actual total profit = 855 (100/57) = Rs. 1500
Quicker Method: Applying the above rule, we have the total profit = 855 (100/(100-5))((3+2)/3)
= 855 (100/95)(5/3)=Rs.1500.
9.Three partners altogether invested Rs. 114,000 in a business. At the end of the year, one got Rs. 337.50, the second Rs. 1125.00 and the third Rs. 675 as profit. How much amount did each invest? What is the percentage of profit?
(a)1.857%
(b)1.856%
(c)1.866%
(d)1.877%
9.(a)
10.Three partners A, B and C together invested Rs. 375000 in a business. At the end of the year, A got Rs. 52000, B got Rs. 65000 and C got Rs. 78000 as profit. How much amount did A invest?
(a) Rs. 100000
(b) Rs. 125000
(c) Rs. 150000
(d) Rs. 160000
10.(a)
Soln:
The ratio of investment = Ratio of profits
= 337.50 : 1125 : 675
= 3375 : 11250 : 6750
Dividing each by 1125, we have the ratio = 3 : 10 : 6.
Shares of the partners = Rs. 114000/(3+10+6)×3,
Rs. 114000/(3+10+6)×10 and Rs.114000/(3+10+6)×6
or, Rs. 18000, Rs. 60000 and Rs. 36000
The required percentage of profit
=(337.5+1125+675)/114000×100=2137.50/1140=1.857%
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