Page 165 - Start Up Mathematics_8 (Non CCE)

10 4 800,
\ = (cross-multiply) Number of workers 10 8
8 x Amount earned (in `) 4,800 x
fi 10 × x = 4,800 × 8

4 800, ¥ 8
fi x = = 3,840
10
\ 8 workers will earn ` 3,840 in 5 days.
Now, for 8 workers:
As the number of workers is same, 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.

3 840, 5
fi = (cross-multiply)
y 9

fi 5 × y = 3,840 × 9 Amount earned (in `) 3,840 5

3 840, ¥ 9 Number of days y 9
fi y = = 6 912,
5
Hence, 8 workers will earn ` 6,912 in 9 days.

Pipes and Cisterns
Given below are some general rules for solving problems related to pipes and cisterns:
(i) If a pipe fills a tank/cistern in x hours, then the part of the tank/cistern
1 1
filled in 1 hour is , or the work done by the inlet in 1 hour is .
x x
(ii) If a pipe empties a full tank in y hours, then the part of the tank emptied

1 Ê - ˆ 1
in 1 hour is , or the work done by the outlet in 1 hour is Á ˜ .
y Ë y ¯ Fig. 10.1

Example 7: A pipe can fill a cistern is 5 hours. The cistern can be emptied by an outlet pipe in 6 hours.
How much time will it take to fill the cistern if both the pipes are opened together?
Solution: The inlet pipe can fill the cistern in 5 hours.

1
\ In 1 hour, the pipe fills of the cistern. Do you know?
5
The outlet pipe can empty the cistern in 6 hours. The author of the famous
book ‘Alice’s Adventures in
1 Wonderland’, Lewis Carroll, was
\ In 1 hour, the pipe empties of the cistern.
6 not only an English author, but
also a mathematician, logician and
1
\ In 1 hour, Ê Á Ë 1 - 1ˆ ˜ = 65- = 30 of the photographer.
6¯
5
30
cistern will be filled.

1 30
\ The cistern will be filled in 1 ÷ = 1 × = 30 hours
30 1

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