Question

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.​

Answer 1

$\huge\bf\fbox\red{Answer:-}$

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

77000 – P = $\frac{P * R * 5}{100}$

⇒ 77000 - P = $\frac{PR}{20}$

⇒ 1540000 - 20P = PR --- (i)

Step 2:

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

68200 - P = $\frac{P * R * 3}{100}$

⇒ 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

⇒ R = 8%

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.

Answer 2

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}

100

PRT

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

77000 – P = \frac{P * R * 5}{100}

100

P∗R∗5

⇒ 77000 - P = \frac{PR}{20}

20

PR

⇒ 1540000 - 20P = PR --- (i)

Step 2:

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

68200 - P =

100

P∗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

⇒ R = 8%

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.

hope it helps !