The ratio between the length and the breadth of a rectangular field is 3 : 2. If only the length is increased by 5 metres, the new area of the field will be 2600 sq. metres. What is the breadth of the rectangular field ?

The perimeter of a rectangular plot of land is 114 metres and its area is 810 square metres.

(i) Take the length of plot as x metres. Use the perimeter 114 m to write the value of the breadth in terms of x.

(ii) Use the values of length, breadth and area to write an equation in x.

(iii) Solve the equation to find the length and breadth of the plot.

(i) ₹ 6,400 were divided equally among x persons. Had this money been divided equally among (x + 14) persons, each would have got ₹ 28 less. Find the value of x.

(ii) ₹ 7,500 were divided equally among a certain number of children. Had there been 20 less children, each would have received ₹ 100 more. Find the original number of children.

A shopkeeper buys x books for ₹ 720.

(i) Write the cost of 1 book in terms of x.

(ii) If the cost per book be ₹ 5 less, the number of books that could be bought for ₹ 720 would be 2 more.

Write down the equation in x and solve it to find x.