Quantitative Reasoning – Practice – Simple interest question – Calculation Intensive or Otherwise!!!

simple interest calculation intensive

PSA_LEVEL-UP_QNR24. Divide Rs 2379 into 3 parts so that their amounts after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:

a) Rs. 759
b) Rs. 792
c) Rs. 818
d) Rs. 828


Let 2379 be divided into principals of P, Q and 2379-(P+Q) which give amounts as below after their respective time periods:

A= P + Simple interest = P + PRT/100 =P(1+R*2/100) –(i)
A= Q + Simple interest = Q + QRT/100 =Q(1+R*3/100) –(ii)
A= [2379-(P+Q)] + Simple interest = [2379-(P+Q)](1+R*4/100) –(iii)

Since all are equal, we can equate two at a time.

(i)=(ii) gives,

P(100+2R)= Q(100+3R)
=> P/Q = 115/110 = 23/22
=>22P=23Q. —-(A)
Similarly, equating (ii) and (iii)
Q/[2379-(P+Q)] = 120/115 = 24/23
=> 23Q= 24[2379] – 24P – 24Q
=>22P+24P= 24[2379] – 22P*24/23
=>23P= 12[2379] – 22*12P/23
=>529P= 12*2379*23 – 22*12P
=>529P+264P= 12*2379*23
=> 793P = 12*2379*23
=> P =828. Option d)

Shortcut to answering this question:
Rs 2379 is divided into 3 parts so that their amounts after 2,3 and 4 years respectively on the same rate of interest. Since first part is invested for minimum time period, its principal amount must be greater than atleast one-third of the principal amount 2379 or 793. Options (c) and (d) could be the answers.

Now from equation (A), you could observe that P= 23Q/22. You would agree that whatever the value of Q, P must be a multiple of 23. [Also 22 & 23 are co-primes and do not have any common factor]. Since 828 is divisible by 23, option (d) is the answer.

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