Question

25. A certain sum of money lent out at simple interest amounts to Rs.1380 in 3 years and Rs.1500 in 5 years. Find the rate percent per annum?​

Answer 1

Step-by-step explanation:

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Answer 2

Given data : A certain sum of money lent out at simple interest amounts to Rs 1380 in 3 years and Rs 1500 in 5 years.

To find : Find the rate percent per annum ?

Solution : Let, principal be P and rate of interest be R.

A/C to question;

• A (amount) = Rs 1380
• T (time period) = 3 years

and

• A = Rs 1500
• T = 5 years

Now, a/c to given data;

For 3 years,

➜ S.I (simple interest) = (P * R * T)/100

➜ S.I (simple interest) = (P * R * 3)/100

➜ S.I (simple interest) = 3PR/100

Here, we know

• Amount = principal + simple interest
• 1380 = P + (3PR/100) ----{1}

Similarly,

For 5 years,

➜ S.I (simple interest) = (P * R * T)/100

➜ S.I (simple interest) = (P * R * 5)/100

➜ S.I (simple interest) = 5PR/100

• Amount = principal + simple interest
• 1500 = P + (5PR/100) ----{2}

Now,

Simple interest for 2 years : subtract eq. {1} from eq. {2}

➜ 1500 - 1380 = P + (5PR/100) - {P + (3PR/100)}

➜ 120= P + (5PR/100) - P - (3PR/100)

➜ 120 = P - P + (5PR/100) - (3PR/100)

➜ 120 = (5PR - 3PR)/100

➜ 120 = 2PR/100

➜ PR/100 = 120/2

➜ PR/100 = 60 ----{3}

Now, put value of PR/100 in eq. {1}

➜ 1380 = P + (3PR/100)

➜ 1380 = P + (3 * 60)

➜ 1380 = P + 180

➜ P = 1380 - 180

➜ P = Rs 1200

To find out the rate of interest, percent per annum : Put value of P in eq. {3}

➜ PR/100 = 60

➜ 1200R/100 = 60

➜ 12R = 60

➜ R = 60/12

➜ R = 5 %

Answer : Hence, the rate of interest, percent per annum is 5 %.

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