increased by 4 cm and the
same. Find the base and the altitude of the triang
18. Two angles of a triangle are in the ratio 4 : 5. If the sum of these angles is equal to the
angle, find the angles of the triangle.
19. A steamer goes downstream from one port to another in 9 hours. It covers the
distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed
steamer in still water and the distance between the ports.
20. The distance between two stations is 300 km. Two motorcyclists start simultaneously
these stations and move towards each other. The speed of one of them is 7 km/h more
that of the other. If the distance between them after 2 hours of their start is 34 km, find
speed of each motorcyclist. Check your solution.
21. Divide 150 into three parts such that the second number is five-sixths the first and the
number is four-fifths the second.
22. Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second
23. Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three
as old as she will be then. Find their present ages.
24. Monu's father is 26 years younger than Monu's grandfather and 29 years older than
The sum of the ages of all the three is 135 years. What is the age of each one of them
25. A man is 10 times older than his grandson. He is also 54 years older than him. Find
present ages.
26. The difference between the ages of two cousins is 10 years 16
Answers
Answer:
Let the triangle (Δ) be ABC
Given : ∠A = 4x
∠B = 5x
∠C = ∠A+∠B
∠C= 4x + 5x = 9x
Here we use angle sum property
⇒ ∠A + ∠B + ∠C = 180°
⇒ 4x + 5x + 9x
⇒ 18x = 180°
⇒ x = \dfrac{180^\circ}{18}
18
180
∘
⇒ x = 10°
Let us verify that
to verify our answer we have to put 10° at the place of 'x'
let's do that
⇒ ∠A + ∠B + ∠C = 180°
⇒ 4x + 5x + 9x = 180°
⇒ 4×10 + 5×10 + 9×10 = 180°
⇒ 40 + 50 + 90 = 180°
⇒ 90 + 90 = 180°
⇒ 180° = 180°
∠A = 4x = 4×10 = 40°
∠B = 5x = 5×10 = 50°
∠C = ∠A+∠B
∠C= 4x + 5x = 9x = 9×10 = 90°
Therefore angles of triangle are 40° , 50° and 50°