Question

What is the interest of Rs. 1080 after 4 years at the rate of Rs. 10%?. After how many years is the interest be same for Rs. 900 at the rate of 12% interest?​

Answer 1

Time = 4 years

Solution :-

Given that

Principal (P) = Rs. 1080

Time (T) = 4 years

Rate of Interest (R) = 10%

We know that

Simple Interest = PTR/100

=> Simple Interest = (1080×4×10)/100

=> Simple Interest = 108×4

=> Simple Interest = Rs. 432

Let the required time be T years

Given Principal = Rs. 900

Rate of interest = 12%

Given that Bothe interests are same.

=> 432 = (900×T×12)/100

=> 432 = 9×T×12

=> 432 = 108 ×T

=> 432/108 = T

=> T = 432/108

=> T = 4 years

Answer :-

The required time is 4 Years

Used formulae:-

→ Simple Interest = PTR/100

• P = Principal
• T = Time
• R = Rate of Interest

Answer 2

Answer:

Given :-

• A sum of Rs 1080 after 4 years at the rate of 10%.
• The interest is same for Rs 900 at the rate of 12% interest.

To Find :-

• What is the simple interest.
• How many years is the interest will be same.

Formula Used :-

$\clubsuit$ Simple Interest or S.I. Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{S.I. =\: \dfrac{P \times R \times T}{100}}}}\: \: \: \bigstar$

$\clubsuit$ Time Period Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{T =\: \dfrac{S.I. \times 100}{P \times R}}}}\: \: \: \bigstar$

where,

• S.I. = Simple Interest
• P = Principal
• R = Rate of Interest
• T = Time Period

Solution :-

First, we have to find the simple interest :

Given :

• Principal (P) = Rs 1080
• Rate of Interest (r) = 10%
• Time Period (t) = 4 years

According to the question by using the formula we get,

$\implies \bf S.I. =\: \dfrac{P \times R \times T}{100}$

$\implies \sf S.I. =\: \dfrac{1080 \times 10 \times 4}{100}$

$\implies \sf S.I. =\: \dfrac{1080 \times 40}{100}$

$\implies \sf S.I. =\: \dfrac{432\cancel{00}}{1\cancel{00}}$

$\implies \sf S.I. =\: \dfrac{432}{1}$

$\implies \sf\bold{\purple{S.I. =\: Rs\: 432}}$

Hence, the simple interest is Rs 432 .

Now, we have to find the time period :

Given :

• Simple Interest (S.I.) = Rs 432
• Principal (P) = Rs 900
• Rate of Interest (r) = 12%

According to the question by using the formula we get,

$\implies \bf T =\: \dfrac{S.I. \times 100}{P \times R}$

$\implies \sf T =\: \dfrac{432 \times 100}{900 \times 12}$

$\implies \sf T =\: \dfrac{\cancel{43200}}{\cancel{10800}}$

$\implies \sf T =\: \dfrac{4}{1}$

$\implies \sf\bold{\red{T =\: 4\: years}}$

$\therefore$ The simple interest is Rs 432 and the time period is 4 years .

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