Question

If Summit drives his car at (5/7)th of his usual speed, he is late by 20 minutes to reach his office from home. Determine usually how long does it take for him to reach his office from home.​

Answer 1

It is given that Rs.30,000 must be invested into two types of bonds with 5% and 7%interest rates.

Let Rs.x be invested in bonds of the first type.

Thus, Rs.(30000−x) will be invested in the other type.

Hence, the amount invested in each type of the bonds can be represented in matrix form with each column corresponding to a different type of bond as :

X=[x30000−x]

A)  Annual interest obtained is Rs.1800.

We know, Interest=100PTR

Here, the time is one year and thus T=1

Hence, the interest obtained after one year can be expressed in matrix representation as -

[x30000−x]⎣⎢⎢⎡10051007⎦⎥⎥⎤=[1800]

⇒  [x×1005+(30000−x)×1007]=[1800]

⇒  1005x+1007(30000−x)=1800

⇒  5x+210000−7x=180000

⇒  −2x=−3000