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Two equal some of money were invested at an annual rate of 10%, One sum at simple interest and other at compound interest, If the difference between the interest after 2 years was Rs.100, What were the sum invested ?
- a)25,000
- b)100000
- c)20,000
- d)10,000
- e)50,000
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two equal some of money were invested at an annual rate of 10%, One su...
Correct Answer :- d
Explanation : Assume X = 100
SI = 120
CI = 121
100 mean difference is 1
200 mean difference is 2
Therefore, 10000 mean difference is 100.
Most Upvoted Answer
Two equal some of money were invested at an annual rate of 10%, One su...
There is a trick that
principle=difference×100/rate×100/rate
only applicable for 2 year
principle=difference×100/rate×100/rate
only applicable for 2 year
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Community Answer
Two equal some of money were invested at an annual rate of 10%, One su...
Given:
- Two equal sums of money were invested.
- The annual rate of interest is 10%.
- One sum is invested at simple interest and the other at compound interest.
- The difference between the interest after 2 years is Rs. 100.
To find:
The sum of money invested.
Solution:
Let's assume the sum of money invested is 'x'.
Step 1: Calculate the simple interest for 2 years.
Simple Interest (SI) = (Principal x Rate x Time) / 100
SI for 2 years = (x x 10 x 2) / 100 = 0.2x
Step 2: Calculate the compound interest for 2 years.
Compound Interest (CI) = Principal x [(1 + Rate/100)^Time - 1]
CI for 2 years = x x [(1 + 10/100)^2 - 1] = x x (1.1^2 - 1) = x x (1.21 - 1) = 0.21x
Step 3: Find the difference between the compound interest and simple interest.
Difference = CI - SI = 0.21x - 0.2x = 0.01x
Given that the difference is Rs. 100, we can set up the equation:
0.01x = 100
Step 4: Solve the equation to find the value of 'x'.
x = 100 / 0.01 = 10,000
Therefore, the sum of money invested is Rs. 10,000.
Answer: Option D.
- Two equal sums of money were invested.
- The annual rate of interest is 10%.
- One sum is invested at simple interest and the other at compound interest.
- The difference between the interest after 2 years is Rs. 100.
To find:
The sum of money invested.
Solution:
Let's assume the sum of money invested is 'x'.
Step 1: Calculate the simple interest for 2 years.
Simple Interest (SI) = (Principal x Rate x Time) / 100
SI for 2 years = (x x 10 x 2) / 100 = 0.2x
Step 2: Calculate the compound interest for 2 years.
Compound Interest (CI) = Principal x [(1 + Rate/100)^Time - 1]
CI for 2 years = x x [(1 + 10/100)^2 - 1] = x x (1.1^2 - 1) = x x (1.21 - 1) = 0.21x
Step 3: Find the difference between the compound interest and simple interest.
Difference = CI - SI = 0.21x - 0.2x = 0.01x
Given that the difference is Rs. 100, we can set up the equation:
0.01x = 100
Step 4: Solve the equation to find the value of 'x'.
x = 100 / 0.01 = 10,000
Therefore, the sum of money invested is Rs. 10,000.
Answer: Option D.
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Two equal some of money were invested at an annual rate of 10%, One sum at simple interest and other at compound interest, If the difference between the interest after 2 years was Rs.100, What were the sum invested ?a)25,000b)100000c)20,000d)10,000e)50,000Correct answer is option 'D'. Can you explain this answer?
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