# Quantitative Reasoning – Practice – Simple interest question – Solve without using any simple interest formulae!!!

PSA_LEVEL-UP_QNR25. An amount of Rs. 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second , 11% p.a. (assume S.I.). If the total interest at end of one year is 9¾ %, then the amount invested in each share was:

a) Rs. 52,500; Rs. 47,500
b) Rs. 62,500; Rs. 37,500
c) Rs. 72,500; Rs. 27,500
d) Rs. 82,500; Rs. 17,500

Ans:

First Method: Let us assume ‘P’ and ‘1,00,000-P’ are the principal invested at 9% and 11% p.a simple interest for time period of 1 year.

Interest earned on first share= P*9*1/100 = 9P/100

Interest earned on second share= (1,00,000-P)*11*1/100 = 11,00,000/100 – 11P/100 = 11,000 – 11P/10

Total interest = 1,00,000* 9.75 * 1/100= 9750.

According to the question,
9750=9P/100 + 11,000 – 11P/10
=>2P/100 = 1250
=>P= 50*1250 = Rs. 62,500

There is no need to calculate the second amount as first amount is unique in each answer option. Option (b)

Second Method:

We use “alligation” concept to solve this and you will realize this is the fastest method given the conditions. The two types of shares at 9% and 11% can be imagined to be the mixture components and 9.75% to be the resultant mixture percentage.

As shown in the above diagram, the amount that must be invested in the two shares must be in the ratio 1.25:0.75 or 5:3. You could calculate the amounts to be 5/8th of 1,00,000 and 3/8th of 1,00,000. But, you could also see that second amount should be a multiple of 3 and only option (b) has a multiple of 3 as the second amount 37,500. [3+7+5= 15 a multiple of 3]. Rest others can be rejected out outright!!!

If you want to have a look at the alligation concepts and different questions, below links would help!

Alligation or Weighted Average

Alligation-Weighted Average [Solved Questions] – Part I

Alligation-Weighted Average [Solved Questions] – Part II

Alligation-Weighted Average [Solved Questions] – Part III

Alligation-Weighted Average [Solved Questions] – Part IV

Alligation-Weighted Average [Solved Questions] – Part V

You can also take the below test to brush up all the learnt concepts!

Hope you are able to utilize both the methods as mentioned in solution while practising various related questions!