Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years? A washing…

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Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years? A washing machine was purchased for Rs. 2100. After 1 year the price were reduced by 5%. What will be pric

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Q1. Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years?

Identify the given values.
Principal ( $P$ ) = Rs. 900
Amount ( $A$ ) = Rs. 1089
Time ( $n$ ) = 2 years
Rate of interest ( $R$ ) = ?
Use the compound interest formula for amount
$A = P\left(1 + \frac{R}{100}\right)^n$ .
Substitute the given values into the formula:
$1089 = 900\left(1 + \frac{R}{100}\right)^2$
Isolate the term with $R$ .
$\frac{1089}{900} = \left(1 + \frac{R}{100}\right)^2$
Simplify the fraction and take the square root of both sides.
$\left(\frac{33}{30}\right)^2 = \left(1 + \frac{R}{100}\right)^2$ $\frac{33}{30} = 1 + \frac{R}{100}$ $\frac{11}{10} = 1 + \frac{R}{100}$
Solve for $R$ .
$\frac{R}{100} = \frac{11}{10} - 1$ $\frac{R}{100} = \frac{11 - 10}{10}$ $\frac{R}{100} = \frac{1}{10}$ $R = \frac{100}{10}$ $R = 10$
The rate of interest is 10% per annum.

The final answer is $\boxed{10\% \text{ P.C.P.A.}}$ .

Q2. A washing machine was purchased for Rs. 2100. After 1 year the price were reduced by 5%. What will be price of machine after 1 year?
Identify the given values.
Original Price ( $P_0$ ) = Rs. 2100
Rate of reduction ( $r$ ) = 5% per year
Time ( $n$ ) = 1 year
Calculate the reduction amount.
$\text{Reduction} = P_0 \times \frac{r}{100}$ $\text{Reduction} = 2100 \times \frac{5}{100}$ $\text{Reduction} = 21 \times 5$ $\text{Reduction} = \text{Rs. } 105$
Calculate the price of the machine after 1 year.
$\text{Price after 1 year} = \text{Original Price} - \text{Reduction}$ $\text{Price after 1 year} = 2100 - 105$ $\text{Price after 1 year} = \text{Rs. } 1995$
The final answer is $\boxed{\text{Rs. } 1995}$ .

Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years? A washing machine was purchased for Rs. 2100. After 1 year the price were reduced by 5%. What will be pric

Step-by-step solution

Identify the given values.

Use the compound interest formula for amount

Isolate the term with $R$ .

Simplify the fraction and take the square root of both sides.

Solve for $R$ .

Identify the given values.

Calculate the reduction amount.

Calculate the price of the machine after 1 year.

Still stuck on this one?

More Mathematics Questions

Find the rate of interest in P.C.P.A. by which Rs. 900 will amounts to Rs. 1089 in two years? A washing machine was purchased for Rs. 2100. After 1 year the price were reduced by 5%. What will be pric

Step-by-step solution

Identify the given values.

Use the compound interest formula for amount

Isolate the term with RRR.

Simplify the fraction and take the square root of both sides.

Solve for RRR.

Identify the given values.

Calculate the reduction amount.

Calculate the price of the machine after 1 year.

Still stuck on this one?

More Mathematics Questions

Isolate the term with $R$ .

Solve for $R$ .