Number problem

[raushan.ravi]

Ram and Shyam started a business with some investment. Ram invested 36% of the total investment and received 9/17th part of the total profit at the end of the year. If Ram stayed in the business throughout the year, for how many months did Shyam invest his amount?

(A) 6
(B) 7
(C) 8
(D) 9

[aravindc78]

Ram and Shyam started a business with some investment. Ram invested 36% of the total investment and received 9/17th part of the total profit at the end of the year. If Ram stayed in the business throughout the year, for how many months did Shyam invest his amount?

(A) 6
(B) 7
(C) 8
(D) 9

Is the answer A, 6 months?

Assume the investment was 100,000. Ram invested 36,000 and stayed in business for the year.

Assume that the profit was P. Ram's share was (9/17) P.

If 36,000 investment gives a profit of (9/17)P, 64,000 investment would yield a profit of:

(64,000 (9/17))/36,000 = (16P/17). However, this is true only if Shyam had also stayed in the business for the entire year.

Actual profit that Shyam got was 1-9/17 = 8P/17. (this is half of 16P/17)

So the number of months that Shyam had invested in is 6 months.

[RonPurewal]

Ram and Shyam started a business with some investment. Ram invested 36% of the total investment and received 9/17th part of the total profit at the end of the year. If Ram stayed in the business throughout the year, for how many months did Shyam invest his amount?

(A) 6
(B) 7
(C) 8
(D) 9

Is the answer A, 6 months?

Assume the investment was 100,000. Ram invested 36,000 and stayed in business for the year.

Assume that the profit was P. Ram's share was (9/17) P.

If 36,000 investment gives a profit of (9/17)P, 64,000 investment would yield a profit of:

(64,000 (9/17))/36,000 = (16P/17). However, this is true only if Shyam had also stayed in the business for the entire year.

Actual profit that Shyam got was 1-9/17 = 8P/17. (this is half of 16P/17)

So the number of months that Shyam had invested in is 6 months.

yeah, that works. or, if you want an easier solution method, just plug in one of the answer choices, compute the profit for that number of months, and then check to see whether it's 9/17 of the total profit.

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in any case:

this problem statement is WAY WAY WAY too vague for the gmat. it's not unreasonable that this problem could appear on the gmat, but it would have to include much more specific text.
in particular, it would have to include all the added parts in green, below:

Ram and Shyam started a business with simultaneous investments. As long as they retained their investment in the business, the investors made profits in proportion to the amount of their investment, at a constant monthly rate. Ram invested 36% of the total investment, and received 9/17 of the total profit at the end of the year. If Ram's investment remained in the business throughout the year, for how many months did Shyam invest his amount?

you can see what i mean - there are ALL KINDS of assumptions that go into this problem, rendering it completely unacceptable as a gmat problem.

this is what i mean about the difference between the gmat and these indian tests. each test has its strengths and vulnerabilities, but the gmat is MUCH more oriented toward testing the traps, pitfalls, and assumptions inherent in problems like this one.

if this were a data sufficiency problem, you can bet they would call you out on the (unjustified) assumption that all the green stuff is true.