# What is the product of the first and third part?

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Divide Rs 9516 into 3 parts so that their amount after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest.
What is the product of the first and third part?

posted Oct 31, 2018

Let the 3 different principles be P1, P2 & P3. Then according to the question:
P1 + P1×R×T1 = P2 + P2×R×T2 = P3 + P3×R×T3
P1/P2 = 1.15/1.1 = 23/22
P2/P3 = 24/23
P1:P2:P3 = 276 : 264 : 253
P1 = 9516 / (276 + 264 + 253) = 9516/793 = 12
Now P1 = 276 × 12 = 3312; P2 = 264 × 12 = 3168
& P3 = 253 × 12 = 3036.

Verification:
3312 + 3312×0.05×2 = 3643.2
3168 + 3168×0.05×3 = 3643.2
3036 + 3036×0.05×4 = 3643.2.

Product of the 1st and the 3rd part:
3312 × 3036 = 10,055,232

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