Answer: Option B
Let the share of each brother be Suresh (S), Bala (B) and Krishnan (K).Total amount = S + B + K = Rs. 7700
Let's assume that the amount is divided in the ratio of a:b:c. Then, we have:S = a/ (a+b+c) * 7700B = b/ (a+b+c) * 7700K = c/ (a+b+c) * 7700
Now, we need to find the ratio of a:b:c such that the simple interest on each part at 5% per annum after 1, 2 and 3 years, respectively remains equal.
Let the simple interest on each part be SI.Then, SI for Suresh = SI for Bala = SI for KrishnanLet the principal amount for Suresh be P, and the time periods for 1, 2 and 3 years be denoted by t1, t2 and t3 respectively. Then, we have:
SI = P * R * Twhere R = 5% per annum = 0.05For Suresh, we have:P = a/ (a+b+c) * 7700T1 = 1 year, T2 = 2 years, T3 = 3 years
SI for Suresh = SI for Bala = SI for Krishnan
a/ (a+b+c) * 7700 * 0.05 * 1 = b/ (a+b+c) * 7700 * 0.05 * 1a/ (a+b+c) * 7700 * 0.05 * 1 = c/ (a+b+c) * 7700 * 0.05 * 1
a = b = c [Canceling out the denominators and simplifying the equation.]
Therefore, the amount is divided equally among the three brothers.
But, the question says that the share of Suresh is more than that of Krishnan.
Let the share of Krishnan be x. Then, we have:Suresh's share = x + 3200 [Since the total amount is divided equally among the three brothers.]
S + B + K = 77002x + 3200 = 77002x = 4500x = 2250
Therefore, Krishnan's share = Rs. 2250Suresh's share = Rs. 2250 + Rs. 3200 = Rs. 5450Hence, the share of Suresh is more than that of Krishnan by Rs. 5450 - Rs. 2250 = Rs. 3200
Therefore, the correct option is B.If you think the solution is wrong then please provide your own solution below in the comments section .