Page 96 - ICSE Math 8

Example 14: A group of 30 students went for a holiday and had food provisions for 9 days. After 2 days,
5 more students joined them. How long will the food provisions last?
Solution: If no more students had joined, the food would have lasted for 9 – 2 = 7 more days. Since
5 more students joined, the food will last for lesser days.
Let the remaining food last for x days. Therefore, x will be the fourth term of the proportion
and 7 will be the third term. As x is less than 7, therefore 30 and 35 are the second and first
terms respectively.
35 7
∴ 35 : 30 = 7 : x 30 =
x
⇒ 35x = 30 × 7 ⇒ x = 7 × 30 = 6
35
∴ The remaining food will last for 6 days.

Proportional Parts

When a given quantity is divided into parts according to a given proportion, the parts obtained are called
proportional parts.

Example 15: Divide 324 chocolates among 3 friends in the ratio 7 : 5 : 6.
7 7
Solution: First friend’s share = 7 + 5 + 6 × 324 = 18 × 324 = 126

5 5
Second friend’s share = 7 + 5 + 6 × 324 = 18 × 324 = 90
6 6
Third friend’s share = 7 + 5 + 6 × 324 = 18 × 324 = 108

∴ The required three shares are 126, 90 and 108 chocolates.

Example 16: Divide 6,250 into three parts in such a way that the first part is 62.5% of the second part and
the ratio between the second and third part is 8 : 12.
Solution: Ratio between the second and third part is 8 : 12.
∴ If the second part is 8, the third part is 12.
62.5 × 8
⇒ First part = 62.5% of second part = = 5
100
∴ Ratio between the three parts = 5 : 8 : 12
Let the first, second and third parts be 5x, 8x and 12x.
6,250
5x + 8x + 12x = 6,250 ⇒ x = = 250
25
∴ First part = 5x = 5 × 250 = 1,250 Second part = 8x = 8 × 250 = 2,000

Third part = 12x = 12 × 250 = 3,000
Example 17: Rahul has ` 20, ` 50 and ` 100 notes in the ratio 5 : 4 : 7. If the total value of the notes is
` 10,000, find the number of each kind of notes.
Solution: Let the number of notes be 5x, 4x and 7x.
Value of 5x notes of ` 20 each = ` (5x × 20) = ` 100x
Value of 4x notes of ` 50 each = ` (4x × 50) = ` 200x
Value of 7x notes of ` 100 each = ` (7x × 100) = ` 700x

⇒ ` (100x + 200x + 700x) = ` 10,000 ⇒ 1,000x = 10,000 ⇒ x = 10
∴ Number of ` 20 notes = 5x = 50
Number of ` 50 notes = 4x = 40 Number of ` 700 notes = 7x = 70

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