Question

Rs 20000 amounts to Rs 25000 in 2 years at a certain rate of interest per annum. in what time will Rs 5528 amount to Rs 11056 at the same rate

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

In 8 years, Rs. 5528 will amount to Rs. 11056 at the same rate (12.5%)

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Rs.20000 amounts to = Rs 25000

In = 2 years

To find :

Time in which Rs. 5528 amount to Rs. 11056 at the same rate of interest.

Solution :

Case I

We need to find the Rate of interest.

Here,

Principal (P) = Rs.20000

Amount = Rs.25000

Time (T) = 2 years.

$\star$ SI = Amount - Principal

$\tt{\Rightarrow25000 - 20000}$

$\tt{\Rightarrow5000}$

Simple Interest (SI) = Rs.5000

We know that,

${\boxed{\mathsf{SI = \frac{Principal \times Rate \times Time}{100}}}}$

$\sf{\implies5000 = \dfrac{20000 \times 2 \times R}{100} }$

$\sf{\implies5000\times100 = 40000\times R}$

$\sf{\implies500000 = 40000 \times R}$

$\sf{\implies \: R = \dfrac{500000}{40000}}$

$\sf{\implies \: R = \dfrac{50{\cancel{0000}}}{4{\cancel{0000}}}}$

$\sf{\implies \: R = \dfrac{50}{4}}$

$\sf{\implies \: R = 12.5}$

${\boxed{\mathsf{\circ \: {Rate = 12.5 \%}}}}$

Case II

We have to find the time.

Here,

Principal (P) = Rs. 5528

Amount = Rs.11056

Rate (R) = 12.5 % (from above)

$\star$SI = Amount - Principal

$\tt{\Rightarrow11056 - 5528}$

$\tt{\Rightarrow5528}$

We know that,

${\boxed{\mathsf{SI = \frac{Principal \times Rate \times Time}{100}}}}$

$\sf{\implies5528 = \dfrac{5528 \times 12.5 \times t}{100} }$

$\sf{\implies5528 \times 100 = 69100 \times T}$

$\sf{\implies552800 = 69100 \times T}$

$\sf{\implies T = \dfrac{552800}{69100}}$

$\sf{\implies T = 8}$

${\boxed{\mathsf{\circ \: {Time = 8 years.}}}}$

$\therefore$In 8 years, Rs. 5528 will amount to Rs. 11056 at the same rate (12.5%)

Answer 2

Rs 20000 amounts to Rs 25000

So Interest = 25k - 20 k = 5k

and time is 2 years and rate per annum let it be x

So x℅ of 20000 × 2 = interest

As x is per annum And its 2 years

x× 200 × 2 = 5000

x × 400 = 5000

x= 12.5

So now

5528 amounts to 11056

interest = 11056 -5528 = 5528

So Interest and amount same

So Rate = 1/time

12.5/100 = 1/time

time = 100/12.5 = 8 years

So in 8 years 55 28 amounts to 11056 at same rate