Multiple choice

Ram invested half of his savings in a bond that paid simple interest for 2 years and received Rs. 550 as interest. He invested the remaining amount in a bond that paid compound interest for 2 years at the same rate of interest and received Rs. 605 as interest. What was the value of his total savings before investing in the two bonds?

  1. Rs. 2,750

  2. Rs. 4,000

  3. Rs. 2,000

  4. Rs. 7,000

  5. Rs. 10,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S be total savings. Half is S/2. SI = (S/2 * R * 2) / 100 = 550 => SR = 55000. CI = S/2 * ((1+R/100)^2 - 1) = 605. S/2 * (2R/100 + R^2/10000) = 605. SR/100 + SR^2/20000 = 605. 550 + (550*R)/200 = 605. 2.75R = 55. R = 20%. SR = 55000 => S*20 = 55000 => S = 2750.

AI explanation

For the first bond, the simple interest equation is P * R * 2 / 100 = 550, so PR = 27500. For the second bond, the compound interest equation is P * [(1 + R/100)^2 - 1] = 605. Substituting R = 27500/P into the second equation gives P * [(1 + 137.5/P)^2 - 1] = 605, which expands to P + 137.5 = 605, yielding P = 1375. The total savings is 2P, which equals Rs. 2,750.

Keep practicing — related questions