Profit and Loss
- 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
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Here , Ratio of their capital = 4 : 8 : 9
Ratio of their share profits = 15 : 8 : 9
Ratio of profits = (Ratio of capital by time).
∴ Ratio of time = Ratio of profit divided by respective capitals.Ratio of time = 15 : 8 : 9 21 18 14 Ratio of time = 5 : 4 : 9 7 9 14
Correct Option: C
Here , Ratio of their capital = 4 : 8 : 9
Ratio of their share profits = 15 : 8 : 9
Ratio of profits = (Ratio of capital by time).
∴ Ratio of time = Ratio of profit divided by respective capitals.Ratio of time = 15 : 8 : 9 21 18 14 Ratio of time = 5 : 4 : 9 7 9 14 Ratio of time = 90 : 56 : 81 [126 is LCM of 7, 9 and 14] 126 126 126
Hence , Ratio of time of A , B and C = 90 : 56 : 81.
- A, B and C enter into a partnership and invest their capital in the ratio 4 : 8 : 9. Their period of investment are in the ratio 6 : 3 : 5. In what ratio would they distribute their profits?
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Given in question , Ratio of their capital = 4 : 8 : 9
Ratio of time period = 6 : 3 : 5
Ratio of profit = Ratio of product of investment and time period.
Ratio of share of profits = A : B : C = (4 × 6) : (8 × 3) : (9 × 5)Correct Option: B
Given in question , Ratio of their capital = 4 : 8 : 9
Ratio of time period = 6 : 3 : 5
Ratio of profit = Ratio of product of investment and time period.
Ratio of share of profits = A : B : C = (4 × 6) : (8 × 3) : (9 × 5) = 24 : 24 : 45
⇒ A : B : C = 8 : 8 : 15
- Ram and Shyam enter into a partnership by contributing capitals in the ratio 16 : 7. After 5 months Ram withdraws. If finally they share profit in the ratio of 5 : 7, find how long Shyam’s capital was used ?
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Given that , Ratio of profit = 5 : 7
Let us assume that Shyam’s capital was used for t months.
Then we can write the ratio of their equivalent capital investment asRam : Shyam = 16 × 5 = 5 7 × t 7
Correct Option: D
Given that , Ratio of profit = 5 : 7
Let us assume that Shyam’s capital was used for t months.
Then we can write the ratio of their equivalent capital investment asRam : Shyam = 16 × 5 = 5 7 × t 7
⇒ t = 16
So, Shyam’s capital was used for 16 months.
- A, B and C together hold a pasture for which they pay a rent at the rate of $ 160 per month. They put on it 70, 50 and 40 cows respectively. A sells (2 / 7) th of his stock to B after 4 months and further 3 months later C sells (2 / 5) th of his stock to A. How much of the rent should A pay in one year?
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On the basis of given details in question ,
Total rent to be paid for one year = 160 × 12 = $ 1920.
This is a case of compound partnership. So, the rent will be shared in proportion to the product of number of cows and time for each partner.
Computing in terms of 1 month,
For A :
For A = (70 × 4) + (50 × 3) + (66 × 5) = 280 + 150 + 330
For A = 760
For B :
For B = 200 + 560 = 760
For C :
For C = 280 + 120 = 400
So, A : B : C = 760 : 760 : 400
A : B : C = 19 : 19 : 10
Sum of ratios = 19 + 19 + 10 = 48Correct Option: C
On the basis of given details in question ,
Total rent to be paid for one year = 160 × 12 = $ 1920.
This is a case of compound partnership. So, the rent will be shared in proportion to the product of number of cows and time for each partner.
Computing in terms of 1 month,
For A :
For A = (70 × 4) + (50 × 3) + (66 × 5) = 280 + 150 + 330
For A = 760
For B :
For B = 200 + 560 = 760
For C :
For C = 280 + 120 = 400
So, A : B : C = 760 : 760 : 400
A : B : C = 19 : 19 : 10
Sum of ratios = 19 + 19 + 10 = 48Rent to be paid = 1920 = 1920 = $ 40 19 + 19 + 10 48
Rent to be paid, by A = 19 × 40 = $ 760
- A and B enter into partnership and invest in stock market trading. Their investments initially were $ 50000 and $ 45000. After 4 months A withdraws half his capital. At the end of 8 months B withdraws half his capital and C joins them with a capital of $ 70000. What should be the ratio in which the profit will be divided at the year-end?
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As per the given in question ,
Investment ratio in terms of 1 month or of their equivalent capitals,A : B : C 
A : B : C = 400,000 : 450,000 : 280,000
Correct Option: B
As per the given in question ,
Investment ratio in terms of 1 month or of their equivalent capitals,A : B : C
A : B : C = 400,000 : 450,000 : 280,000
A : B : C = 40 : 45 : 28
The profits will be distributed in the above ratio i.e., 40 : 45 : 28.
