Question

. A sum of money becomes Rs.
283.75 and Rs. 306-25 in 3 years
and 5 years respectively, then find
the annual rate of interest.
(a) Rs. 90
(b) Rs. 105
(c) Rs. 95
(d) Rs. 70​

Answer 1

Answer:

• The annual rate of interest is 4.5%.

Step-by-step explanation:

Given that:

• A sum of money becomes Rs. 283.75 and Rs. 306.25 in 3 years and 5 years respectively.

To Find:

• The annual rate of interest.

Formula used:

• SI = (P × R × T)/100
• A = P + (P × R × T)/100

Where,

• SI = Simple interest
• P = Principal
• R = Rate of interest
• T = Time
• A = Amount

Amount after 3 years,

⟶ P + (P × R × 3)/100 = 283.75

Taking 100 common.

⟶ 100P + 3PR = 100(283.75)

⟶ P(100 + 3R) = 28375

⟶ P = 28375/(100 + 3R) _____(i)

Amount after 5 years,

⟶ P + (P × R × 5)/100 = 306.25

Taking 100 common.

⟶ 100P + 5PR = 100(306.25)

⟶ P(100 + 5R) = 30625

⟶ P = 30625/(100 + 5R) _____(ii)

Comparing eqⁿ(i) and eqⁿ(ii).

⟶ 28375/(100 + 3R) = 30625/(100 + 5R)

Cross multiplication.

⟶ (100 + 5R)28375 = 30625(100 + 3R)

⟶ 2837500 + 141875R = 3062500 + 91875R

⟶ 141875R - 91875R = 3062500 - 2837500

⟶ 50000R = 225000

⟶ R = 225000/50000

⟶ R = 4.5

Hence,

• The annual rate of interest is 4.5%.

Answer 2

Answer:

Given :-

• A sum of money becomes Rs 283.75 and Rs 306.25 in 3 years and 5 years respectively.

To Find :-

• What is the annual rate of interest.

Formula Used :-

$\clubsuit$ Amount Formula :

$\longmapsto \sf\boxed{\bold{\pink{Amount =\: P + \bigg(\dfrac{P \times R \times T}{100}\bigg)}}}$

where,

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

Solution :-

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: amount\: for\: 3\: months\: :-}}}}}$

Given :

• Amount = Rs 283.75
• Time = 3 years

According to the question by using the formula we get,

$\implies \sf 283.75 =\: P + \bigg(\dfrac{P \times R \times 3}{100}\bigg)$

$\implies \sf 100(283.75) =\: 100P + 3PR$

$\implies \sf 100 \times 283.75 =\: P(100 + 3R)$

$\implies \sf 28375 =\: P(100 + 3R)$

$\implies \sf \dfrac{28375}{100 + 3R} =\: P$

$\implies \sf\bold{\green{P =\: \dfrac{28375}{100 + 3R}\: ------\: (Equation\: No\: 1)}}$

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: amount\: for\: 5\: years\: :-}}}}}$

Given :

• Amount = Rs 306.25
• Time = 5 years

According to the question by using the formula we get,

$\implies \sf 306.25 =\: P + \bigg(\dfrac{P \times R \times 5}{100}\bigg)$

$\implies \sf 100(306.25) =\: 100P + 5PR$

$\implies \sf 100 \times 306.25 =\: P(100 + 5R)$

$\implies \sf 30625 =\: P(100 + 5R)$

$\implies \sf \dfrac{30625}{100 + 5R} =\: P$

$\implies \sf\bold{\green{P =\: \dfrac{30625}{100 + 5R}\: ------\: (Equation\: No\: 2)}}$

Now, from the equation no 1 and 2 we get,

$\longrightarrow \sf \dfrac{28375}{100 + 3R} =\: \dfrac{30625}{100 + 5R}$

By doing cross multiplication we get,

$\longrightarrow \sf 28375(100 + 5R) =\: 30625(100 + 3R)$

$\longrightarrow \sf 2837500 + 141875R =\: 3062500 + 91875R$

$\longrightarrow \sf 141875R - 91875R =\: 3062500 - 2837500$

$\longrightarrow \sf 50000R =\: 225000$

$\longrightarrow \sf R =\: \dfrac{225\cancel{000}}{50\cancel{000}}$

$\longrightarrow \sf R =\: \dfrac{\cancel{225}}{\cancel{50}}$

$\longrightarrow \sf R =\: \dfrac{\cancel{45}}{\cancel{10}}$

$\longrightarrow \sf \bold{\red{R =\: 4.5\%}}$

$\therefore$ The annual rate of interest is 4.5%.