Page 158 - Start Up Mathematics_8 (Non CCE)

Solution: Let the number of bananas that Aditya can buy at the increased price be x dozen.
Note that with the same amount of money, more the price of bananas, lesser number of bananas
can be bought.
So, the number of bananas is in inverse variation with the price of bananas.

12 40
\ = (cross-multiply)
x 30
fi 40x = 12 × 30 Number of bananas 12 x
(in dozen)
12 30¥
fi x = = 9 Price (in `) 30 30 + 10 = 40
40
Hence, Aditya can buy 9 dozen bananas, when the price of bananas is increased by ` 10 per dozen.

EXERCISE 9.2
1. Which of the following are in inverse variation with each other?
(a) The number of burgers (n) you can buy with ` 150 and the cost (c) of each burger.
(b) The time taken to finish a given work and the number of men doing that work.
(c) The amount of petrol used and the distance travelled by a car.
(d) The number of children in a birthday party and the amount of food consumed.
(e) Time taken to cover a given distance with variation in speed of a vehicle.
2. In which of the given tables, x and y are in inverse variation with each other?
(a) x 2 4 3 8 12 (b) x 6 4 12 30 15

y 16 8 12 4 3 y 10 15 5 2 4

3. Fill in the missing entries if x and y vary inversely:
(a) x 45 ... 10 ... 30 (b) x ... 12 16 ... 15

y 2 15 ... 18 ... y 10 20 ... 30 ...

4. A hostel mess has provisions for 200 students for 30 days. If 100 new students join the hostel, how
long will the provisions last?
5. If Kinjal reads 8 pages daily, she can finish a book in 15 days. How many pages does Kinjal read
daily if she finishes the book in 10 days?
6. Five spraying machines working together can finish painting a house in 36 minutes. If 2 machines
break down, then in how much time can the remaining machines complete the job?
7. Rahul and Chunky start together from Delhi in their own cars for Shimla. Rahul drives at an average
speed of 60 km/h and reaches Shimla in 9 hours. If Chunky drives at an average speed of 54 km/h,
how much time will he take to reach Shimla?
8. Reena has enough money to buy 10 kg of potatoes worth ` 18/kg with the same money. How many
kilograms of potatoes can she buy if the price of potatoes increases to ` 20/kg?
9. A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed
using 20 bottles in each box, how many boxes would be filled?
10. If x is in inverse variation with y and
(a) x = 4, y = 6, find x, when y = 12.
(b) x = 7, y = 4, find y, when x = 2.
(c) x = 20, find y when constant of variation is 300.
(d) y = 16, find x when constant of variation is 176.

150