**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!

Alligation-Weighted Average Test.

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