Page 172 - ICSE Math 8

13. In a competitive exam, there are 90 multiple choice questions. 4 marks are awarded for every correct
answer, 2 marks are deducted for every wrong answer and 0.5 marks is deducted for every unattempted
question from the total score of correct answers. If a student leaves 10 questions unattempted and scores
a total of 195 marks, how many of his answers were correct?
14. Sunny has three boxes of different types of sweets. Box I weighs 2 1 kg more than Box II and
2
1 3
Box III weighs 10 kg more than Box II. The total weight of the boxes is 54 kg. What is the weight
4 4
of Box I?
15. A steamer goes downstream and covers the distance between two ports in 4 hours. It covers the same
–1
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
16. If times a number is 10 more than the number, find the number.
4
17. The side of square A is 3 cm longer than twice the side of square B. The difference in their areas is
144 sq. cm. Find the sides of the two squares.
5
18. 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 is decreased by 2 cm, the area of the triangle remains the same. Find the altitude and
the base of the original triangle.
19. The distance between two stations is 482 km. Two trains start simultaneously from these stations
on parallel tracks towards each other. The speed of one of them is greater than that of the other by
–1
4 km h . If the distance between them after 3 hours is 20 km, find the speed of each train.

Linear Inequation
An inequation is an algebraic statement which states the inequality of two expressions. The symbols of
inequality are ‘<’ which means ‘is less than’, ‘≤’ means ‘is less than or equal to’, ‘>’ means ‘is greater than’
and ‘≥’ means ‘is greater than or equal to’. An inequation in which the highest power of the variable is one
is known as a linear inequation. A linear inequation in one variable x is of the form ax + b ≥ c where a,
b and c are constants and a ≠ 0. In the above form, the symbol ‘≥’ can be replaced by any other symbol of
inequality.

Replacement Set and Solution Set
The replacement set is a given set from which the values of the variable have to
be selected in order to make an inequation true. It is also known as domain of the Maths Info
variable. Solution set is the set of values of the variable from the replacement set Truth or Solution set is always
which when substituted makes the inequation true. It is also known as truth set. a subset of a replacement set,
For example, if x ≤ 2 and x ∈ {0, 1, 2, 3, 4, 5, 6}, then the replacement set is {0, 1, 2, i.e., Truth set ⊆ replacement set.
3, 4, 5, 6}. Out of this set 0, 1 and 2 make the inequation true. So, the solution set is
{0, 1, 2}.

Rules for Solving Inequations

The following rules hold for inequations.
(a) The symbol of inequality remains unchanged if the same number is added to or subtracted from both
sides of the inequation. Symbolically, this can be represented as:

If a < b, then a + c < b + c or a – c < b – c.

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