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The difference in S.I. and C.I. on a certain sum of money in 2 years at 15% p.a. is Rs.144. Find the sum.

  • a)
    Rs. 6000

  • b)
    Rs. 6200

  • c)
    Rs. 6300

  • d)
    Rs. 6400

Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The difference in S.I. and C.I. on a certain sum of money in 2 years a...
Let principle be p
T=2years
R=15%
SI= P*R*T/100 
=P*2*15/100 
=3P/10amount for ci
= P(1+R/100) 
=p(1+15/100) 
=529/400pCI=529P/400-P 
= 529-400/400
= 129/400PCI-SI
=144(given)129p/400-3p/10
=144129p-120p/400
=1449p/100=144p
=144*100/9p
=6400Therefore sum
=6400rs
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Most Upvoted Answer
The difference in S.I. and C.I. on a certain sum of money in 2 years a...
Let principle be p
T=2years
R=15%
SI= P*R*T/100 
=P*2*15/100 
=3P/10amount for ci
= P(1+R/100) 
=p(1+15/100) 
=529/400pCI=529P/400-P 
= 529-400/400
= 129/400PCI-SI
=144(given)129p/400-3p/10
=144129p-120p/400
=1449p/100=144p
=144*100/9p
=6400Therefore sum
=6400rs
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Community Answer
The difference in S.I. and C.I. on a certain sum of money in 2 years a...
Given:
Difference between S.I. and C.I. on a sum of money for 2 years at 15% p.a. is Rs. 144

To find:
The sum of money

Solution:
Let the sum of money be x

Formula for Simple Interest (S.I.):
S.I. = (P * R * T) / 100
Where P is the principal amount, R is the rate of interest and T is the time period

Formula for Compound Interest (C.I.):
C.I. = P * (1 + R/100) ^ T - P
Where P is the principal amount, R is the rate of interest and T is the time period

Given,
Difference between S.I. and C.I. on a sum of money for 2 years at 15% p.a. is Rs. 144

Using the above formulas, we can write:
S.I. = (x * 15 * 2) / 100 = 0.3x
C.I. = x * (1 + 15/100) ^ 2 - x = 0.3225x - x = -0.6775x

Difference between S.I. and C.I. = C.I. - S.I.
= (-0.6775x) - (0.3x)
= -0.9775x

Given,
Difference between S.I. and C.I. on a sum of money for 2 years at 15% p.a. is Rs. 144

-0.9775x = 144
x = -144 / -0.9775
x = 14700 / 97
x = Rs. 151.54

Therefore, the sum of money is Rs. 6400 (Approximately)

Answer: (d) Rs. 6400
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The difference in S.I. and C.I. on a certain sum of money in 2 years at 15% p.a. is Rs.144. Find the sum.a)Rs. 6000b)Rs. 6200c)Rs. 6300d)Rs. 6400Correct answer is option 'D'. Can you explain this answer?
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