Manipur Board Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 3: EXERCISE 4.3

The area of a rectangular garden is increased by $55 {\mathrm{m}}^2$, if its length is reduced by $2 \mathrm{m}$ and the breadth is increased by $5 \mathrm{m}$. If the length is increased by $3 \mathrm{m}$ and the breadth by $2 \mathrm{m}$ the area is increased by $70 {\mathrm{m}}^2$. Find the area of the rectangular garden in ${\mathrm{m}}^2$.

A rectangle is of the same area as another which is $6 \mathrm{m}$ long and $4 \mathrm{m}$ narrow. It is also of the same area as a third rectangle which is $8 \mathrm{m}$ long and $5 \mathrm{m}$ narrow. Find the area of the rectangle in ${\mathrm{m}}^2$.

An annual income of $₹1200$ is derived from two sums invested, one at $4\%$ and the other at $6\%$ per annum simple interest. If the rates of interest are changed to $5\%$ and $7\%$ per annum simple interest respectively, the annual income derived from the investments is $₹1450$. Find the sums invested in $₹$.

A man invested $₹36000$, a part of it at $12\%$ and the rest at $15\%$ per annum simple interest. If he received a total annual interest of $₹4890$, how much did he invest at each rate?

In a classroom, there are a number of benches. If $4$ students sit on each bench, five benches are left vacant; and if $3$ students sit on each bench, $4$ students are left standing. Find the number of benches and students in the classroom.

The sum of a two-digit number and the number obtained by reversing the digits is $110$. If the difference of the digits of the number is $4$, find the number. How many such numbers are there?

The ratio of incomes of two persons is $9:7$ and the ratio of their expenditures is $4:3$. If each of them saves $₹2000$ per month, find their monthly incomes.

A two-digit number is obtained either by multiplying the sum of the digits by $8$ and adding $1$, or by multiplying the difference of the digits by $13$ and adding $2$. Find the number. How many such numbers are there?