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A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?
- a)15%, Rs. 1100
- b)20%, Rs. 1000
- c)17%, Rs. 1400
- d)20%, Rs. 1100
- e)22%, Rs. 900
Correct answer is option 'B'. Can you explain this answer?
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A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. ...
Given:
- Sum amounts to Rs. 1400 in 2 years
- Sum amounts to Rs. 1600 in 3 years
To find:
- Rate of simple interest
- Principal sum
Let's assume the principal sum as P and the rate of interest as R.
Formula:
Simple Interest (SI) = (P * R * T) / 100
Where:
- P is the principal sum
- R is the rate of interest
- T is the time period in years
Solution:
We have two equations based on the given information:
1) P + (P * R * 2) / 100 = 1400 (Equation 1)
2) P + (P * R * 3) / 100 = 1600 (Equation 2)
Simplifying Equation 1:
100P + 2PR = 140000
100P = 140000 - 2PR
P = (140000 - 2PR) / 100
P = 1400 - 2PR (Equation 3)
Simplifying Equation 2:
100P + 3PR = 160000
100P = 160000 - 3PR
P = (160000 - 3PR) / 100
P = 1600 - 3PR (Equation 4)
Subtracting Equation 4 from Equation 3:
P - P = (1400 - 2PR) - (1600 - 3PR)
0 = 1400 - 1600 + 2PR - 3PR
0 = -200 - PR
PR = -200 (Equation 5)
Since the rate of interest cannot be negative, we can ignore the negative sign in Equation 5.
Now substitute the value of PR in Equation 3:
P = 1400 - 2(-200)
P = 1400 + 400
P = 1800
Therefore, the principal sum is Rs. 1800.
Substituting the values of P and R in Equation 1 to find the rate of interest:
1800 + (1800 * R * 2) / 100 = 1400
1800 + 36R = 1400
36R = 1400 - 1800
36R = -400
R = -400 / 36
R = -11.11
Again, we ignore the negative sign as the rate of interest cannot be negative.
Therefore, the rate of simple interest is 11.11%.
Hence, the correct answer is option B) 20% and Rs. 1000.
- Sum amounts to Rs. 1400 in 2 years
- Sum amounts to Rs. 1600 in 3 years
To find:
- Rate of simple interest
- Principal sum
Let's assume the principal sum as P and the rate of interest as R.
Formula:
Simple Interest (SI) = (P * R * T) / 100
Where:
- P is the principal sum
- R is the rate of interest
- T is the time period in years
Solution:
We have two equations based on the given information:
1) P + (P * R * 2) / 100 = 1400 (Equation 1)
2) P + (P * R * 3) / 100 = 1600 (Equation 2)
Simplifying Equation 1:
100P + 2PR = 140000
100P = 140000 - 2PR
P = (140000 - 2PR) / 100
P = 1400 - 2PR (Equation 3)
Simplifying Equation 2:
100P + 3PR = 160000
100P = 160000 - 3PR
P = (160000 - 3PR) / 100
P = 1600 - 3PR (Equation 4)
Subtracting Equation 4 from Equation 3:
P - P = (1400 - 2PR) - (1600 - 3PR)
0 = 1400 - 1600 + 2PR - 3PR
0 = -200 - PR
PR = -200 (Equation 5)
Since the rate of interest cannot be negative, we can ignore the negative sign in Equation 5.
Now substitute the value of PR in Equation 3:
P = 1400 - 2(-200)
P = 1400 + 400
P = 1800
Therefore, the principal sum is Rs. 1800.
Substituting the values of P and R in Equation 1 to find the rate of interest:
1800 + (1800 * R * 2) / 100 = 1400
1800 + 36R = 1400
36R = 1400 - 1800
36R = -400
R = -400 / 36
R = -11.11
Again, we ignore the negative sign as the rate of interest cannot be negative.
Therefore, the rate of simple interest is 11.11%.
Hence, the correct answer is option B) 20% and Rs. 1000.
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A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer?
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A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer?.
A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum amounts to Rs. 1400 in 2 years and Rs. 1600 in 3 years. Find the rate of simple interest and the sum(principal)?a)15%, Rs. 1100b)20%, Rs. 1000c)17%, Rs. 1400d)20%, Rs. 1100e)22%, Rs. 900Correct answer is option 'B'. Can you explain this answer?.
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