What will be the percentage share of Y in the profit earned by X, Y and Z together ?
I. X, Y and Z invested a total amount of Rs. 25,000 for a period of two years.
II. The profit earned at the end of 2 years is 30%.
III. The amount invested by Y is equal to the amount invested by X and Z together.
Answer : Option A
From III, Y = X + Z `rArr Y's investment is 50%
`:.` Share of Y is 50%.
Thus, I and II are redundant .
`:.` Correct answer is (A).
Three friends, P, Q and R started a partnership business investing money in he ratio of 5 : 4 : 2 respectively for a period of 3 years. What is the amount received by P as his share in the total profit ?
I. Total amount invested in he business in Rs. 22,000
II. profit earned at the end of 3 years is `3/8` of the total investment ..
III. he average amount of profit earned per year is Rs. 2750.
Answer : Option B
I and II give , profit after 3 years = Rs. `(3/8 xx 22000)` = Rs. 8250.
From III also , profit after 3 years = Rs. (2750 x 3) = Rs. 8250
`:.` P's share = Rs. `(8250 xx 5/11)` = Rs. 3750.
Thus , (either III is redundant ) or (I and II are redundant ).
`:. ` Correct answer is (B).
A and B are partners in a business . A contributes `1/4 `of the capital for 15 months and B received `2/3` of the profit . For how long B's money was used ?
Answer : Option C
Let the total profit be Rs. z . Then ,
B's share = Rs. `(2z)/(3)`, A's share = Rs. `(z - (2z)/(3))` = Rs. `z/3`
`:.` A : B = `z/3 : (2z)/(3) ` = 1 : 2
Let the total capital be Rs. `x` and suppose B's money was used for `x` months. Then ,
`(1/4 x xx 15)/(3/4 x xx y)` = `1/2` `hArr y = ((12 xx 2)/(3))` = 10.
Thus, B's money was used for 10 months
A and B shared a business with initial investments in the ratio 14 : 15 and their annual profit were in the ratio 7 : 6
If A invested the money for 10 months , for how many months did B invest his money ?
Answer : Option C
Suppose A invested Rs. 14`x` for 10 months and B invested Rs. 15`x` for y months . Then
` (14x xx 10)/(15x xx y) = 7/6 hArr y = 840/105` = 8
Hence , B invested the money for 8 months.