Page 100 - ICSE Math 7

Example 19: There are 26 students in a group. They have food to last for 63 days. For how many
students will the same food last for 39 days?
Solution: Number of students and amount of food are in inverse variation.

For 63 days, food lasts for 26 students.
∴ For 1 day, food will last for 26 × 63 students.
26 × 63
∴ For 39 days, food will last for = 42 students.
39
Example 20: In a military camp, there is food for 64 soldiers to last for 15 days. After 5 days,
16 more soldiers join the camp. For how many days will the remaining food last?
Solution: Number of soldiers and amount of food are in inverse variation.

After 5 days, there is food in the camp for 10 (15 – 5) days for 64 soldiers.
New number of soldiers = 64 + 16 = 80
For 64 soldiers, food lasts for 10 days.
∴ For 1 soldier, food will last for 10 × 64 days.
10 × 64
∴ For 80 soldiers, food will last for = 8 days.
80
–1
Example 21: A car running at a speed of 56 km h can cover a certain distance in 5 hours. What
should be the speed of the car if the same distance is to be covered in 4 hours?

Solution: Speed of car and time required to cover a certain distance are in inverse variation.
To cover a certain distance in 5 hours, speed required = 56 km h –1
∴ To cover the same distance in 1 hour, speed required = (56 × 5) km h –1

56 × 5 –1 –1
∴ To cover the same distance in 4 hours, speed required = km h = 70 km h
4

EXERCISE 7.3

1. A car uses 30 litres of petrol to cover a distance of 375 km. How many litres will be needed to
cover a distance of 1,200 km?
2. An alloy is formed by mixing 4.5 g copper and 2.8 g zinc. How much alloy of similar kind can
be formed by using 13.5 g copper?
3. In a summer camp, there was provision for soaps for 45 students for 30 days. For how many
students will the same soaps last for 27 days?
4. A hostel has enough food to feed 115 children for 88 days. After a week, 20 more children join
the hostel. For how many days will the remaining food last?
–1
5. A bike can cover a certain distance with a speed of 56 km h in 6 hours. What should be the
speed of the bike if the same distance is to be covered in 8 hours?
6. For 27 students 198 L milk is sufficient for 22 days. For how many students will 105 L of milk
be sufficient for 35 days?
7. An army camp had provision for food for 600 soldiers for 30 days. However, the number of
soldiers who attended the camp was less than 600, so the food was sufficient for 48 days. Find
the number of soldiers who attended the camp.
8. If 28 identical boxes weight 84 kg, then how many boxes will weight 126 kg?
9. Saurabh pays ` 9,000 as rent for 4 months. How much will he have to pay for a whole year, if
the rent per month remains the same?

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