Question

8. What sum of money invested at 7.5% p.a. simple interest for 2 years produces twice
as much interest as 9600 in 3 years 6 months at 10% p.a. simple interest?​

Answer 1

Answer :-

44880

Explanation :-

In first one's

$\sf{P_1 =9600}$

$\sf{R_1 =10}$

$\sf{T_1 =3 \: years \: 6 \: months=3\dfrac{1}{3}}$

$\sf{ \dfrac{7}{2}years}$

Therefore,Simple Interest will be :-

$\sf{\dfrac{P \times R\times T} {100}}$

$\rightarrow \sf{\dfrac{1900 \times 10 \times 7}{100 \times 2}}$

$\sf{ \rightarrow Rs.3360}$

In second one's

$\sf{Interest \:for \: 2years => 3360 \times 2}$

$\sf{ \rightarrow 6720}$

$\sf{R_2 = 7}$

$\sf{T_2 = 2years}$

$\sf{Therefore,P_2\: will\: be}$

$\rightarrow\sf{\dfrac{SI \times 100}{R \times T}}$

$\rightarrow \sf{ \dfrac{6720 \times 100}{7.5 \times 2}}$

$\rightarrow \sf{44880}$

Hence, the sum of money invested is 44880

Answer 2

First Case:

Principal (P1) = Rs 9600

Rate (R1) = 10%

Period = (T) = 3 years 6 months

Simple interest = (P × R × T) / 100

= (9600 × 10 × 7) / (100 × 2)

We get,

= Rs 3360

Second case:

Simple interest = Rs 3360 × 2

= Rs 6720

Rate (R) = 7.5% p.a. and

Period (T) = 2 years

Therefore,

Principal = (S.I × 100) / (R × T)

= (6720 × 100) / (7.5 × 2)

= Rs (6720 × 100 × 10) / (75 × 2)

= 6720000 / 150

We get,

= Rs 44800

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