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A sum of Rs. 7,930 is divided into three parts and given on loan at 5% SI to A, B and C for 2 , 3 and 4 years respectively. If amount obtained from all three are equal after their respective periods of loan, then what amount was lent to B?
- a)1320
- b)3300
- c)2640
- d)3960
Correct answer is option 'C'. Can you explain this answer?
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A sum of Rs. 7,930 is divided into three parts and given on loan at 5%...
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A sum of Rs. 7,930 is divided into three parts and given on loan at 5%...
To solve this problem, we can use the formula for calculating Simple Interest:
Simple Interest = (Principal * Rate * Time) / 100
Let's assume the amount lent to A, B, and C are x, y, and z respectively.
Given:
Total amount lent = Rs. 7,930
Rate of interest = 5%
From the given information, we can form the following equations:
Equation 1: x + y + z = 7,930 (Total amount lent is divided into three parts)
Equation 2: (x * 5 * 2) / 100 = (y * 5 * 3) / 100 = (z * 5 * 4) / 100 (Amount obtained from all three are equal after their respective periods of loan)
Simplifying Equation 2, we get:
10x = 15y = 20z
Let's assume the common ratio between x, y, and z is k. So, we can rewrite the equation as:
10k = 15k = 20k
From this, we can find the value of k:
10k + 15k + 20k = 7,930
45k = 7,930
k = 7,930 / 45
k = 176.22
Now, we can substitute the value of k in the equations to find the values of x, y, and z:
x = 10k = 10 * 176.22 = 1762.2
y = 15k = 15 * 176.22 = 2643.3
z = 20k = 20 * 176.22 = 3524.4
Therefore, the amount lent to B is Rs. 2643.3, which is option C.
Simple Interest = (Principal * Rate * Time) / 100
Let's assume the amount lent to A, B, and C are x, y, and z respectively.
Given:
Total amount lent = Rs. 7,930
Rate of interest = 5%
From the given information, we can form the following equations:
Equation 1: x + y + z = 7,930 (Total amount lent is divided into three parts)
Equation 2: (x * 5 * 2) / 100 = (y * 5 * 3) / 100 = (z * 5 * 4) / 100 (Amount obtained from all three are equal after their respective periods of loan)
Simplifying Equation 2, we get:
10x = 15y = 20z
Let's assume the common ratio between x, y, and z is k. So, we can rewrite the equation as:
10k = 15k = 20k
From this, we can find the value of k:
10k + 15k + 20k = 7,930
45k = 7,930
k = 7,930 / 45
k = 176.22
Now, we can substitute the value of k in the equations to find the values of x, y, and z:
x = 10k = 10 * 176.22 = 1762.2
y = 15k = 15 * 176.22 = 2643.3
z = 20k = 20 * 176.22 = 3524.4
Therefore, the amount lent to B is Rs. 2643.3, which is option C.
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