Page 95 - ICSE Math 8

26 39 Number of toffees
∴ x = 67.50 ⇒ 39x = 26 × 67.50 Cost (in `)
26 × 67.50 26 39
⇒ x = = 45
39 x 67.50
∴ 45 toffees can be bought.

Inverse Proportion Quantity 1 Quantity 2
When two quantities are related in such a way that an increase or decrease in p r
the first quantity causes a decrease or increase in the second quantity, then the
two quantities are said to be in inverse proportion. For inverse proportion, write q s
the quantities in tabular form.
Quantity 1 Quantity 2
Invert one of the ratios and then cross-multiply to get qs = pr.
p s

q r
Example 12: If 8 students can complete a particular work in 15 days, then how many students will complete
the same work in 20 days?
Solution: Number of students and time required to complete the Students Days
work are in inverse proportion as more the number
of students involved, lesser will be the time required. 8 15
Let x be the number of students required to complete x 20
the work in 20 days.
Invert one of the ratios to get: Try This
8 20
= ⇒ 20x = 8 × 15 Find the value of x if 3.6, 18, 5
x 15 and x are in:
15 × 8
⇒ x = 20 = 6 (a) direct proportion
∴ 6 students will finish the work in 20 days. (b) inverse proportion

Rule of Three

Rule of three is a method to find the fourth term of a proportion when the other three terms are given.
Follow the given steps to solve problems by the rule of three.
(a) Let the quantity to be obtained be x. Write it as fourth term of the proportion.
(b) Out of the three given quantities, the quantity which is of the same kind as the quantity to be obtained
is the third term.
(c) Find out whether x will be greater or lesser than the third term. If x is greater, then out of the two
remaining quantities, the greater quantity will be the second term and the smaller quantity will be the
first term. If x is smaller, then the smaller quantity will be the second term and the greater quantity will
be the first term.
Example 13: 16 boys can eat a basket full of fruits in 1 min 39 s. How much time will 9 boys take to finish
the same basket?
Solution: Let x be the fourth term of the proportion. So, 1 min 39 s = 99 s will be the third term.
As lesser the number of boys, more time will be taken to finish the fruits, therefore x is greater
than the third term 99. So, make 16 the second term and 9 the first term.

9 : 16 = 99 : x
9 99 16 × 99
⇒ 16 = x ⇒ 9x = 16 × 99 ⇒ x = 9 = 176

∴ 9 boys will take 2 min 56 s.

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