Suhit borrowed a sum of $6300 from Vikas at the rate of 14% for 3 yr.

Question

Suhit borrowed a sum of $6300 from Vikas at the rate of 14% for 3 yr. He then added some more money to the borrowed sum and lent it to Mohit at the rate of 16% of simple interest for the same time. If Suhit gained $618 in the whole transaction, then what sum did he lend to Mohit?

(A) $6000
(B) $6800
(C) $7200
(D) $7500
(E) $7800

Show Answer

Official Answer

B

(A) $6000
(B) $6800
(C) $7200
(D) $7500
(E) $7800

elgunp · Accepted Answer

$618 gain he made comes from 2% (16%-14%) of the principal for 3 years + 16% of the additional money lent to Mohit. Accordingly, 6300*3*2%+3*16%*x=618; x= 500; 500+6300=6800

Answer B

sthahvi · Answer

the answer should be 6800 right, but I want to ask is there a shorter way too do this without all the calculations ?

twobagels · Answer

-6300*1.42 + x*1.48 = 618

the above equals about 6,462, but I'm not sure I followed the question well.

charlie1195 · Answer

I'll take a stab at this question.

If we see, the $618 that Suhit is earning, he is earning it from the difference in the interest amount from the two transactions.

We know that:
Amount lent by Vikas (V) to Suhit (S) = $6300
Amount lent by S to Mohit (M) = $6300 + $x

From the question, we know that 
Interest on amount from V to S = 14% for 3 years.
Hence, interest = (6300 * 14 * 3)/100

Interest on amount from S to M = 14% for 3 years
Hence, interest = ((6300+x) * 16 * 3)/100

The difference between these two expressions is $618
((6300+x) * 16 * 3)/100 - (6300 * 14 * 3)/100 = 618
48x = 240*100
x = 500

Hence, the amount that Suhit lent to Mohit = $6300 + $500 = $6800

usuallysmiling · Answer

Can someone PLEASE explain what's wrong with the below approach:
(6300+x)(1+0.16*3)-6300(1+0.14*3)=618

gmatshay · Answer

I got trapped because I assumed Suhit borrowed money at Compounded Interest, and subsequently lent it at Simple Interest. This was because I saw the 16% was specifically mentioned to be simple, but there was no information about the 14%. In the GMAT, are we to assume interest is added simply and not compounded unless mentioned otherwise?

Bunuel · Answer

It should be:

(6300 + x)(0.16 * 3) - 6300(0.14 * 3) = 618
x = 500

So, the amount Suhit lent to Mohit is:
6300 + x = 6300 + 500 = 6800

Answer: B.

Bunuel · Answer

Questions on the real exam will be worded precisely, with no room for ambiguity.

usuallysmiling · Answer

Understood. Here we just have included the interest impact. But since in the question it is written "If Suhit gained $618 in the whole transaction", which means the entire transaction cycle, which would also ultimately include the principal amount, Logically I thought the below approach would work: (P+x)(1+R%n)(total he would receive)- P(1+R%n)(total he would pay)= Gain . Please let me know, where am I getting wrong

Bunuel

It should be:

(6300 + x)(0.16 * 3) - 6300(0.14 * 3) = 618
x = 500

So, the amount Suhit lent to Mohit is:
6300 + x = 6300 + 500 = 6800

Answer: B.

Bunuel · Answer

Here is correct (intended) interpreation:

Suhit borrowed a sum of $6300 from Vikas at the rate of 14% for 3 yr. He then added some more money to the borrowed sum and lent it to Mohit at the rate of 16% of simple interest for the same time. If Suhit gained $618 in the whole transaction, then what sum did he lend to Mohit?

(A) $6000
(B) $6800
(C) $7200
(D) $7500
(E) $7800

Show Answer

Official Answer

B

Simple interest for 3 yr:

Interest Suhit pays Vikas
= 6300 * 14/100 * 3 =
= 2646

Let x be the sum Suhit lent to Mohit.

Interest Suhit earns from Mohit
= x * 16/100 * 3 = 
= 0.48x

Net gain comes only from the interest difference:
0.48x - 2646 = 618
x = 6800

Answer: $6800 (B)

Suhit borrowed a sum of $6300 from Vikas at the rate of 14% for 3 yr.

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Suhit borrowed a sum of $6300 from Vikas at the rate of 14% for 3 yr.

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