A sum of Rs. 7930 is divided into three parts and given on loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then B received a loan of

Let's solve the problem step by step:

Step 1: Let's assume that B received a loan of x rupees.

Step 2: Now, let's calculate the simple interest for each person using the formula: Simple Interest = (Principal * Rate * Time) / 100

For person A: Principal = x rupees Rate = 5% Time = 2 years Simple Interest for A = (x * 5 * 2) / 100 = 10x/100 = x/10

For person B: Principal = x rupees Rate = 5% Time = 3 years Simple Interest for B = (x * 5 * 3) / 100 = 15x/100 = 3x/20

For person C: Principal = x rupees Rate = 5% Time = 4 years Simple Interest for C = (x * 5 * 4) / 100 = 20x/100 = x/5

Step 3: According to the problem, the amounts of all three are equal after their respective periods of loan. So, we can set up the equation:

Principal + Simple Interest = Total Amount

For person A: Principal + Simple Interest for A = x + x/10 = 11x/10

For person B: Principal + Simple Interest for B = x + 3x/20 = 23x/20

For person C: Principal + Simple Interest for C = x + x/5 = 6x/5

Step 4: Since the amounts of all three are equal, we can equate the expressions:

11x/10 = 23x/20 = 6x/5

Step 5: Let's solve the equation to find the value of x:

11x/10 = 23x/20

Multiply both sides by 20 to eliminate the denominators:

22x = 23x

Subtract 22x from both sides:

0 = x

Step 6: Since x = 0, it means that B did not receive any loan. Therefore, B received a loan of 0 rupees.

So, B received a loan of 0 rupees.