Page 105 - ICSE Math 8

Example 10: 10 workers can earn ` 48,000 in 5 days. What amount will 8 workers earn in 9 days?
Solution: In 5 days:
Since the number of days are fixed, lesser the number of workers, less is the amount earned.
Thus, the number of workers are in the direct variation with the amount earned.
Let the amount earned by 8 workers in 5 days be x.
10 48 000,
\ = (cross-multiply) Number of workers 10 8
8 x Amount earned (in `) 48,000 x
fi 10 × x = 48,000 × 8
48 000 8, ×
fi x = = 38,400
10
\ 8 workers will earn ` 38,400 in 5 days.
Now, for 8 workers:
As the number of workers is fixed, more the number of days they work, more the amount they
will earn.
Thus, the amount earned is in direct variation with the number of days worked.
Let the amount earned in 9 days be y.
38 400, 5
fi = (cross-multiply)
y 9
×
,
fi 5 × y = 38,400 × 9 fi y = 38 400 9 = 69 120,
5
Hence, 8 workers will earn ` 69,120 in 9 days.

Example 11: A and B do a piece of work in 10 days, B and C do it in 15 days and C and B do it in 12 days.
(a) In how many days will A, B and C finish it working together?
(b) In how many days will each one of them finish it working alone?
Solution: Time taken by (A + B) to finish the work = 10 days
1
∴ (A + B)’s 1 day’s work = …(i)
10
Time taken by (B + C) to finish the work = 15 days
1
∴ (B + C)’s 1 day’s work = …(ii)
15
Time taken by (C + A) to finish the work = 12 days
1
∴ (C + A)’s 1 day’s work = 12 …(iii)
Adding (i), (ii) and (iii), we get
1 1 1 6 + 4 + 5 15 1
2(A + B + C)’s 1 day’s work = + + = = =
10 15 12 60 60 4
1 1 1
(a) (A + B + C)’s 1 day’s work = × =
4 2 8
∴ A, B and C will complete the work in 8 days
(b) C’s 1 day’s work = (A + B + C)’s one day work – (A + B)’s 1 day work
1 1 5 – 4 1
= – = =
8 10 40 40
∴ C will complete the work in 40 days
1 1 15 – 8 7 120 1
A’s 1 day’s work = – = = ∴ A will finish the work in or 12 days
8 15 120 120 7 2
1 1 3 – 2 1
B’s 1 days work = = – = = ∴ B will finish the work in 24 days.
8 12 24 24

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