Question

13. The denominator of a rational number is greater than its numerator by 7. If the numerator
is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find
the original number.
14. In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the
2
numerator and to the denominator, the new fraction is - Find the original fraction.
3
15. The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and
the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the
original rectangle. Find the length and the breadth of the original rectangle.
16. The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the
dimensions of the rectangle.
17. An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude be
increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the
same. Find the base and the altitude of the triangle.
18. Two angles of a triangle are in the ratio 4:5. If the sum of these angles is equal to the third
angle, find the angles of the triangle.
19. A steamer goes downstream from one port to another in 9 hours. It covers the same
distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the
steamer in still water and the distance between the ports.
20. The distance between two stations is 300 km. Two motorcyclists start simultaneously from
these stations and move towards each other. The speed of one of them is 7 km/h more than
that of the other. If the distance between them after 2 hours of their start is 34 km, find the
speed of each motorcyclist. Check your solution.
21. Dividie 150 into th​

Answer 1

Answer:

The denominator of a rational number is greater than its numerator by 7. If the numerator

is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find

the original number.

14. In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the

2

numerator and to the denominator, the new fraction is - Find the original fraction.

3

15. The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and

the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the

original rectangle. Find the length and the breadth of the original rectangle.

16. The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the

dimensions of the rectangle.

17. An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude be

increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the