Page 149 - Start Up Mathematics_8 (Non CCE)

16. A steamer goes downstream and covers the distance between two ports in 4 hours. It covers the same
distance upstream in 5 hours. If the speed of the stream is 2 km/h, find the speed of the steamer in
still water and the distance between the two ports.
[Hint: Speed upstream = speed in still water – speed of the stream]

5
17. If times a number results in the value of the number increasing by 10, find the number.
4
18. The side of one square is 3 cm longer than twice the side of the second square. The difference in
their areas is 144 sq. cm. Find the sides of the two squares.
19. Sita and Gita start walking from the same point on the road but in opposite directions. If Sita walks
at the speed of 5 km/h and Gita at a speed of 4 km/h, in how much time will they be 27 km apart?
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20. An altitude of a triangle is times the length of its corresponding base. If the altitude is increased by
3
4 cm and the base decreased by 2 cm, the area of the triangle remains the same. Find the altitude
and the base of the triangle.
21. The distance between two stations is 482 km. Two trains start simultaneously from these stations
on parallel tracks to cross each other. The speed of one of them is greater than that of the other
by 4 km/h. If the distance between the two trains after 3 hours is 20 km, find the speed of each
train.

Brainstorming Reason It Out!

A banana costs ` 6, while an apple costs One day Pulkit said “Two days ago, I was
` 5. How many apples and bananas can 23 years old and next year, I will be 26
be purchased for a total of ` 32? years old.” How is this possible?

AT a Glance

1. An equation consisting of only linear polynomials is called a linear equation.
2. The solution of a linear equation is the value of the variable which satisfies the equation.
3. Rules for solving a linear equation:
(a) Same number can be added on both the sides of the equation without affecting the equality.
(b) Same number can be subtracted from both the sides of the equation without affecting the equality.
(c) Both sides of the equation can be multiplied by the same number ‘m’ without affecting the equality.
(d) Both sides of the equation can be divided by the same number ‘m’ (m π 0) without affecting the
equality.
4. Any term of the equation can be transposed to the other side by changing its sign.
px q+ l
5. To solve equations of the form = , we cross-multiply to get a linear equation, i.e., m(px + q)
rx t+ m
= l(rx + t) and solve.

Review Exercises

Multiple ChoiCe Questions
1. The linear equation that represents the statement “4 times the number of coins in my pocket plus 5 more
is 29” is:
(a) 4x – 5 = 29 (b) 4x + 29 = 5 (c) 4x + 5 = 29 (d) None of these

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