P Q and R entered into a partnership by investing certain amount for 12 months T months and 12 ndash...........

Quantitative Aptitude (SBI-PO) Data Sufficiency

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

P, Q and R entered into a partnership by investing certain amount for 12 months, T months and (12 – T) months respectively. Find the value of T.

Statement I: Q invested 50% more amount than the amount invested by P and R invested twice of the amount invested by Q.

Statement II: At the end of the partnership, total profit earned by them is Rs. 700 and Q gets Rs. 100 as his share of profit.

Statement III: At the end of the partnership, profit share of P and R is in the ratio of 1 : 2

Only the data given in statements I and II together is sufficient to answer the question.

Only the data given in statements I and III together is sufficient to answer the question.

The data given in any two statements together is sufficient to answer the question.

The data given in either statement I and II together or statement I and III together is sufficient to answer the question.

The data given in all three statements I, II and III together is not sufficient to answer the question.

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Explanation:

Time Period of P’s investment = 12 months
Time Period of Q’s investment = T months
Time Period of R’s investment = (12 – T) months
Statement I:
Let the amount invested by P = Rs. 2a
Then, amount invested by Q = 150% of 2a = Rs. 3a
And amount invested by R = 2 × 3a = Rs. 6a
Thus, respective ratio of investments of P, Q and R is
= 12 × 2a : T × 3a : (12 – T) × 6a
= 8 : T : (24 – 2T)
We cannot find the value of T from the above ratio. Thus, statement I alone is not sufficient.
Statement II:
Total profit earned by P, Q and R = Rs. 700
Profit earned by Q = Rs. 100
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Since, there is nothing given about the investments of P, Q and R so statement II alone is not sufficient.
Statement III:
Ratio of profit share of P and R = 1 : 2
So, statement III is not sufficient.
Statement I and II together:
Ratio of amount invested by P, Q and R = 8 : T : (24 – 2T)
Total profit earned by P, Q and R = Rs. 700
Profit earned by Q = Rs. 100
So, profit earned by P and R together = Rs. 600
Thus,
⇒ 3200 – 200T = 600T
⇒ 3200 = 8T
⇒ T = 4 months
Thus, statement I and II together are sufficient to answer the question.
Statement I and III together:
Ratio of amount invested by P, Q and R = 8 : T : (24 – 2T)
Ratio of profit share of P and R = 1 : 2
i.e., =
⇒ 16 = 24 – 2T
⇒ T = 4 months
Thus, statement I and III together are sufficient to answer the question.
Hence, option 4 is the correct answer.