Answer:375

Step-by-step explanation:

LET the sum be Rs.x

Amount after 3 years on Rs.x at 20% per annum when interest is compounded annually

=

P

(

1

+

R

100

)

T

=

x

(

1

+

20

100

)

3

=

x

(

120

100

)

3

=

x

(

6

5

)

3

Compound Interest =

x

(

6

5

)

3

−

x

=

x

[

(

6

5

)

3

−

1

]

=

x

[

216

125

−

1

]

=

91

x

125

Simple Interest =

PRT

100

=

x

×

20

×

3

100

=

3

x

5

=P(1+R100)T=x(1+20100)3=x(120100)3=x(65)3Compound Interest = x(65)3−x=x[(65)3−1]=x[216125−1]=91x125Simple Interest = PRT100=x×20×3100=3x5

Given that DIFFERENCE between compound interest and simple interest is Rs.48

91

x

125

−

3

x

5

=

48

91

x

−

75

x

125

=

48

16

x

125

=

48

x

=

48

×

125

16

=

3

×

125

=

Rs. 375

91x125−3x5=4891x−75x125=4816x125=48x=48×12516=3×125=Rs. 375

i.e, the sum is Rs.375

--------------------------------------------------------------------------------------

Solution 2

---------------------------------------------------------------------------------------

The difference between compound interest and simple interest on Rs. P for 3 years at R% per annum

=

P

(

R

100

)

2

(

R

100

+

3

)

=P(R100)2(R100+3)

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P

(

R

100

)

2

(

R

100

+

3

)

=

48

P

(

20

100

)

2

(

20

100

+

3

)

=

48

P

(

1

5

)

2

(

1

5

+

3

)

=

48

P

(

1

25

)

(

16

5

)

=

48

P

=

48

×

25

×

5

16

=

3

×

25

×

5

=

375