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An amount is lent at x% p.a. simple interest for two years. Instead, had it been lent at 2x% p.a. simple interest for y more years, then the interest would have been five times the earlier interest. Find the value of y.
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'B'. Can you explain this answer?
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To solve this question, we can set up the equation based on the given information and then solve for the value of y.
Let's assume the principal amount is P.
The interest for the first scenario, where the amount is lent at y% p.a. for two years, can be calculated using the simple interest formula:
Interest = (P * y * 2) / 100
In the second scenario, the amount is lent at 2y% p.a. for y more years. Therefore, the interest for this scenario can be calculated as:
Interest = (P * 2y * (2 + y)) / 100
According to the question, the interest in the second scenario is five times the interest in the first scenario. So, we can set up the equation:
(P * 2y * (2 + y)) / 100 = 5 * (P * y * 2) / 100
Simplifying the equation:
2y * (2 + y) = 10y
Expanding the left side:
4y + 2y^2 = 10y
Rearranging the equation:
2y^2 - 6y = 0
Factoring out 2y:
2y (y - 3) = 0
Setting each factor equal to zero:
2y = 0 or y - 3 = 0
Solving for y:
y = 0 or y = 3
Since the principal amount cannot be zero, the value of y is 3.
Therefore, the correct answer is option (B) 3.
Let's assume the principal amount is P.
The interest for the first scenario, where the amount is lent at y% p.a. for two years, can be calculated using the simple interest formula:
Interest = (P * y * 2) / 100
In the second scenario, the amount is lent at 2y% p.a. for y more years. Therefore, the interest for this scenario can be calculated as:
Interest = (P * 2y * (2 + y)) / 100
According to the question, the interest in the second scenario is five times the interest in the first scenario. So, we can set up the equation:
(P * 2y * (2 + y)) / 100 = 5 * (P * y * 2) / 100
Simplifying the equation:
2y * (2 + y) = 10y
Expanding the left side:
4y + 2y^2 = 10y
Rearranging the equation:
2y^2 - 6y = 0
Factoring out 2y:
2y (y - 3) = 0
Setting each factor equal to zero:
2y = 0 or y - 3 = 0
Solving for y:
y = 0 or y = 3
Since the principal amount cannot be zero, the value of y is 3.
Therefore, the correct answer is option (B) 3.
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