Page 137 - Maths Skills - 8

Direct and Inverse Proportions 135

Example 3: The cost of 57 metres of cloth is ` 199.50. What length of this can be purchased for ` 353.50?

Solution: Let x metres of length be purchased for ` 353.50. The above data can be put in a table as under:
Length in metre (p) 57 x
Cost in rupees (q) 199.50 353.50

Clearly, more amount will fetch more metres. So, it is a case of Alternative Approach
direct proportion. cost meter
Hence, the ratio between the length (p) and corresponding cost (q) 199.50 57
is the same. 353.50 x

So, we have x 353 50
.
57 x Here, =
.
= 57 199 50
199.50 353.50 57 353 50.
57 × 353.50 or x
⇒ x = = 101 199 50.
199.50 or x = 101 meter
\ 101 m length of cloth can be purchased in ` 353.50.

Exercise 9.1

1. If p varies directly as q in each of the following cases, then complete the following tables.
(i) p 1.5 3 4.5 – – (ii) p 7 9 – 15 – (iii) p 20 25 – 40 –

q – 4 – 24 30 q 28 – 44 – 76 q – 10 4 – 12
2. Look at the following tables and find in which cases do p and q vary directly.
(i) p 3 4 5 7 8 (ii) p 7 5 9 11 13 (iii) p 4 6 9 13 15

q 12 16 20 28 32 q 21 15 27 33 39 q 10 15 27 39 45
3. If 15 sheets of paper weigh 125 grams, how many sheets of the same quality of paper would weigh 15 kg?
4. 415 US dollars cost ` 19297.50. How many dollars can one buy for ` 29016?
5. A typewriter types at a speed of 40 words per minute. How much time will it take to type 2720 words?
6. A motor car covers a distance of 48 km in 60 minutes. How long will it take to run 180 km non-stop?
7. The second class train fare for a distance of 400 km is ` 250. Find the second class fare from Delhi to
Allahabad, if the distance is 640 km?
8. A teacher is paid ` 1300 per week (for 5 working days). If in a certain month she is paid ` 6500, find the
number of days did she teach?
9. If 7 apples cost ` 40, what do 70 apples cost?

10. A private taxi charges a fare of ` 375 for 250 km. How much it would travel for ` 412.50?
11. A worker is paid ` 880 for working 8 days. If his total wages during a month are ` 2860, for how many
days did he work?
12. If 18.75 metres of a uniform wire weighs 12 kg, what will be the length of 36 kg of the same wire?
1
13. 12 men can dig 7 metres long trench in one day. How many men should be employed for digging 30
2
metres long trench of the same type in one day?
14. In 15 days, the earth picks up 3.3 × 10 pounds of dust from the atmosphere. How much dust it will pick
8
up in 50 days?