Page 97 - ICSE Math 8

EXERCISE 8.3

1. If 4 kg apples cost ` 35, what is the cost of 7 kg apples?

2. Shreya bought 12 pens for ` 36. How many pens can she buy for ` 54?
3. Given that 14 women can cook a required quantity of food in 9 hours. How long will it take to cook the
same amount of food by 6 women?
4. A military camp had provision for soaps for 120 soldiers for 36 days. After 6 days, 20 soldiers left the
camp. How long will the soaps last?
5. If 18 women can harvest a field in (15x + 18) days and 33 women can harvest the same field in 9x days,
then find the value of x.
6. A factory has 225 labourers who take 72 days to complete the planned production. If the production has
to be completed in 90 days, how many labourers will be required?
7. Shobhit divided ` 84,500 amongst his 3 children in the ratio 9 : 11 : 6. How much did each child get?
1 4 2
8. Divide 2,407 coins in the ratio 2 : 1 : 1 .
5
3
5
9. Renuka bought bananas in the ratio of 3 : 7 : 5 on three particular days. If she bought 55 bananas on the
third day, find:
(a) the total number of bananas bought
(b) the number of bananas bought on the other two days
10. Rahul, Karan and Sameer have a total sum of ` 24,000. Rahul and Karan have it in the ratio
11 : 13 and Sameer has 25% of the total of Rahul and Karan. Find the money each of them have.

AT A GLANCE

¾ Ratio is a relation between any two quantities of the same kind and in the same unit, which expresses
how many times one quantity is of the other quantity.
¾ To divide a quantity a in the ratio x : y,

First part =   x   × a and Second part =   y   × a
 x + y   x + y 
¾ To divide a quantity a in the ratio x : y : z,
 x   y   z 
First part =   × a , Second part =   × a and Third part =   × a
yz
yz
yz
 x + +   x + +   x + + 
¾ Four quantities are said to be in proportion if the ratio of the first to the second quantity is same as the
ratio of the third to the fourth quantity.
¾ If three quantities a, b and c are such that a : b = b : c, then a, b and c are said to be in continued proportion.
The second quantity is called mean proportional and the third quantity is called third proportional.
¾ When two quantities are related in such a way that an increase or decrease in the first quantity causes an
increase or decrease in the second quantity, then the two quantities are said to be in direct proportion.

¾ When two quantities are related in such a way that an increase or decrease in the first quantity causes a
decrease or increase in the second quantity, then the two quantities are said to be in inverse proportion.

MENTAL MATHS

1. Write the ratio between 10 kg and 100 g.
2. Which ratio is greater—17 : 50 or 2 : 3?

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