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.
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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.
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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 !