Question

Ratio of numerical value of rate of interest and time period is 5: 1. Man invested Rs. 2600 and gets Rs. 3250 as simple interest. Find the value of X, if man invested Rs. (2600 + X) at same rate of interest on C.I. for two years and get Rs. 1800 as interest?​

Answer 1

Answer: X = Rs. 600

Step-by-step explanation:

The ratio of rate of interest and time period, R:T = 5:1.

So, let the rate of interest be “5x”% & time period be “x” years.

Step 1:

For Simple interest:

Principal, P = Rs. 2600

Simple Interest, S.I. = Rs. 3250

We know,

S.I. = [PRT] / 100

⇒ 3250 = [2600 * 5x * x] / 100

⇒ x² = 3250 / [26*5]

⇒ x = √[25] = 5

∴ R = 5x = 5*5 = 25 %

And ,

T = x = 5 years

Step 2:

For compound interest:

Principal, P = Rs. [2600+X]

Compound Interest, C.I. = Rs. 1800

Time, n = 2 years

Rate of interest same as that in case of S.I. = 25%

We know,

C.I. = P [(1+R/100)ⁿ - 1]

⇒ 1800 = [2600+X] [(1+25/100)² - 1]

⇒ 1800 = [2600+X] [1.5625 - 1]

⇒ 1800 = [2600+X] [0.5625]

⇒ 1800 = 1462.5 + 0.5625X

⇒ 0.5625X = 337.5  

⇒ X = 600

Thus, the value of X is Rs. 600 .