Math, asked by wiftahsin, 5 days ago

A certain sum amounts to Rs 77000 in 5 years and to Rs 68200 in 3 years , under simple interest. If the rate of Interest increased by 2%, in how many years will it double itself.

Answers

Answered by ItzMissLegend

146

$\huge \sf \colorbox{gold}{Answer♡}$

If the rate of interest is increased by 2% points then the principal of Rs. 55000 will be doubled in 10 years.

Step-by-step explanation:

Required Formulas:

Simple Interest = Amount – Principal =

$\frac{PRT}{100}$

Step 1:

Let the sum of money be denoted as “P” and the rate of interest be denoted as “R”%.

It is given that the sum amounts to Rs. 77000 in 5 years, so using the formula, we get

Step 2:

Also given, the sum amounts to Rs. 68200 in 3 years, so using the formula, we get

$68200−P= 100P∗R∗3100P∗R∗3$

⇒ 6820000 - 100P = 3PR

⇒ 6820000 - 100P = 3 [1540000 - 20P] [substituting from (i)]

⇒ 6820000 - 100P = 4620000 - 60P

⇒ 40P = 6820000 - 4620000

⇒ 40P = 2200000

⇒ P = Rs. 55000

Substituting the value of P in eq. (i), we get

1540000 - (20 * 55000) = 55000 * R

⇒ 1540000 - 110000 = 55000 * R

⇒ R = 440000/55000

Step 3:

It is given that the sum of money will get doubled

i.e., ∵ P = Rs. 55000 then Amount = 55000 * 2 = Rs. 110000

∴ Simple Interest = 110000 - 55000 = Rs. 55000

The rate of intrest is increased by 2% i.e., now the rate of inteest becomes = 2 + 8 = 10%

Let the time for this case be denoted as "T" years.

Therefore,

$55000= 10055000∗10∗T$

⇒ T = 10 years

Answered by llMissSwagll

$\huge \sf{ \underline{ \pink{ \underline{ \blue{ \underline{ \pink{AnSwEr}}}}}}} \red❁$