Veeru invested Rs 10000 at 5% simple annual interest

Question

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

A 10
B 11
C 12
D 13
E 14

A 10
B 11
C 12
D 13
E 14

sivatx2 · Answer

Amount = P(1+ nR/100) 
Veeru's current principal when Joy is ready to invest (after 2 years) will be 11,000 (add five hundred per year for 5%)

Let n be the number of years after the first 2 years when Veeru invested.

11000(1+5n/100) = 8000(1+ 10n/100)
11(100+5n)/100 = 8(100+10n)/100
1100 +55n = 800+80
25n = 300
n= 12
So total number of years since Veeru started to invest is n+2 = 14.
=> The answer choice is E. 
Please correct the answer choice or change the question accordingly.

DashingNightmare2 · Answer

Simple Interest = \frac{P*R*T }{100}

Veeru's per year interest =  \frac{10000*5*1}{100}  =500
 Joy's per year interest =  \frac{8000*10*1}{100}  =800

Difference between Joy interest and veeru interest =300.

Initially veeru invested for 2 years, interest for 2 years = Rs 1000
Difference between veeru's and Joy's initial amount =2000
So total Rs 3000 needs to be covered, it can be covered in 3000/300 from joys joining date
= 10 years from joy's investment date
Veeru invested for 2 more years, hence total year =10+2 = 12
Hence  C

Fdambro294 · Answer

One can think of the problem as a person would about a problem involving a car trying to catch up to a slower one, driving in the same direction.

The key trap is the question stem: how many years after VEERU’s investment do they catch up.

Veeru invests 10,000 at 5% interest per year.

He gets a 2 year head start.

So at end of year 2/beginning of year 3 he has 10,000 + 500 + 500 = 11,000.

He gains 500 a year

Joy starts at beginning of year 3 with 8,000 at 10% interest. She gains 800 a year.

The “gap” that Joy must catch up to in order to make the investments equals is: 11,000 - 8,000 = 3,000

Joy will gain 800 a year.

Veeru will gain 500 a year.

The “relative gain” (akin to relative speed) is +300 a year that Joy will catch up.

3,000 / 300 = 10 years for Joy to catch up.

But this is 10 years from when JOY started her investment.

Veeru started 2 years earlier.

Total time from the start of VEERU’s investment = 2 + 10 =

12 (C)

Posted from my mobile device

rvgmat12 · Answer

10^4 + 5/100*10^4 (x) = 8*10^3+8*10^3*10/100(x-2)

10 + x/2 = 8 + 4/5(x-2)

x = 12

Vetrick · Answer

The catching up calculations using the difference in Principal and difference in interest is interesting.

But since this is just simple interest problem, I saw this problem as an Arithmetic Progression problem and used Tn = a + (n-1) d

Let n be the no of years of veeru's investment, so number years of Joy's investment is (n-2)

10000 + (n-1) 500 = 8000 + (n-3) 800

Solving for n, I get 13.

Bunuel  @chetan4u - Does this mean that at the beginning of 13th year of the Veeru's investment, the amounts become equal and therefore it is 12 years after veeru's investment ?

GMATCoachBen · Answer

Vetrick : Yes, your method and logic work — the beginning of the 13th year means that it is 12 years after Veeru's investment.

I find it simpler to just solve directly for what it's asking for — have "n" or "T" represent the years AFTER Veeru's investment.

Many people use this Simple Interest formula: I = PRT (where I = interest, P = Principal, R = Rate, T = Time in years)

CrackverbalGMAT · Answer

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

A 10
B 11
C 12
D 13
E 14

The Simple interest Veeru gets every year is 5 % of 10,000 i.e 500

Joy gets 10 % of 8000 i.e Rs 800 every year as simple interest.

Assume that 'n' years after Veeru's investment, their balances (P + S.I) are equal. It's also given that Joy invested 2 years after Veeru.

The interest, Veeru got after 'n' years is 500*n, and Joy got 500(n-2) as interest after n-2 years.

Equating their total balance after 'n' years

10,000 + 500 n = 8000 + 800(n-2)

2000 = 800n - 1600 -500n
3600 = 300n
n = 12 years.

Option C is the answer.

Thanks,
  Clifin J Francis,
GMAT SME

Vetrick · Answer

Got it. Thank you  GMATCoachBen .

And  CrackVerbal  's reply above is also helpful. Instead of using n-1 & n-3, I could use n & n-2. Thank you.

bumpbot · Answer

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Veeru invested Rs 10000 at 5% simple annual interest

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