Q. 414.5( 2 Votes )

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2,800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Help age India as donation. Which value is reflected in this question?(CBSE 2016)

Answer :

Given: There are two types of bonds paying 10% and 12% as interest.


To find: the amount invested by the trust in both the bonds using given conditions


Let the amount invested in the first and second bond be x and y respectively.


In first case:


The rate of interest in first and second bond be 10% and 12 % respectively







In second case:


The amounted invested in both the bonds gets interchanged


So, the amount in first and second bond is y and x respectively


The rate of interest in first and second bond be 10% and 12 % respectively









To solve these equations and get values of x, y, we have:


AX = B where,




Now, check whether system has unique solution or not:



= 10 × 10 – 12 × 12


= 100 – 144


= -44



The system of the equation is consistent and have unique solution


AX = B


X = A-1 B


Formula used:














Thus,




X = A-1 B








Solutions of the equations are x = 10000, y = 15000


Hence, the amount invested in the first and second bond is 10000 and 15000 respectively

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