Charu invested Rs.12000 at 10% simple interest. After 2.5 years

Question

Charu invested Rs.12000 at 10% simple interest. After 2.5 years Seema also invested Rs. 10000 at 16% rate of interest (simple interest). In how many years after Seema’s investment, their amounts (Principal + Interest) become equal?

A. 10
B. 10.5
C. 12,5
D. 15
C. 18

A. 10
B. 10.5
C. 12,5
D. 15
C. 18

SaquibHGMATWhiz · Answer

Solution:

Let us assume that  n  years after Seema's investment the amount of Charu and Seems becomes equal.

Charu's amount  n  years after Seema's investment  =12000+\frac{12000	imes 10	imes (n+2.5)}{100}=12000+1200(n+2.5) 
Seems's amount  n  years after Seema's investment  =10000+\frac{10000	imes 16	imes n}{100}=10000+1600n

According to the question,  12000+1200(n+2.5)=10000+1600n 
 ⇒12000+1200n+3000=10000+1600n 
 ⇒1200n-1600n=10000-12000-3000 
 ⇒-400n=-5000 
 ⇒400n=5000 
 ⇒n=\frac{5000}{400} 
 ⇒n=12.5

Hence the right answer is    Option C

KarishmaB · Answer

This is similar to a relative speed question.

Charu earns 1200 in interest every year so in the first 2.5 years, she earns Rs. 3000. So at the end of 2.5 years, 
Charu's total is 2000 (she invests 2000 more than Seema) + 3000 = 5000 extra.

Seema earns 1600 in interest every year. So she earns Rs 400 more than Charu then on and must make up the 5000 difference between them.

Time taken by Seema to make up this difference = 5000/400 = 12.5 years

Answer (C)

southpaw21 · Answer

karishma , I like your approach. Can you help in finding mistake in my solution please?

Charu invested 2.5 years before Seema and given her 10% interest, she would've made 3000 interest on her amount in that time. This makes her investment to be 12000 + 3000 = 15000.

Now, Charu has 15000 amount to invest while Seema starts off with 10000.

Total amount with Charu should equal to Seema's in 't' years

Hence, 
15000 *   = 10000 *

Solving above gives me t=50 which obviously is wrong.

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Charu invested Rs.12000 at 10% simple interest. After 2.5 years

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