Page 155 - Start Up Mathematics_8 (Non CCE)

Example 3: A machine can pack 45 boxes in 5 hours. How many boxes can it pack in 12 hours?
Solution: Let the number of boxes packed in 12 hours be x.

Note that more the number of boxes, more the number Number of boxes 45 x
of hours the machine will take to pack them. So, the Number of hours 5 12
number of boxes and number of hours are in direct
variation.
45 5
\ = (cross-multiply)
x 12

fi 5x = 45 × 12
45 12¥
fi x = = 9 × 12 = 108
5

Hence, the machine can pack 108 boxes in 12 hours.
Example 4: If 7 women or 5 men earn ` 875 in a day. How much will 5 women and 10 men earn in one
day?
7
Solution: 5 men = 7 women fi 1 man = 5 women Number of women 7 19
7 Earning (in `) 875 x
fi 10 men = × 10 = 14 women
5
\ 10 men and 5 women = 14 women + 5 women = 19 women
Let ` x be the earning by 5 women and 10 men in one day.
\ ` x will also be the earning of 19 women in one day.
Note that more the number of women, more will be the earning. So, number of women is in
direct variation with the earnings.
7 875
\ = (cross-multiply)
19 x

fi 7x = 875 × 19
875 19¥
fi x = = 2,375
7
Hence, 5 women and 10 men earn ` 2,375 in one day.

EXERCISE 9.1

1. Which of the following show direct variation?
(a) Height of a child (x) and his weight (y) as he grows
(b) Distance travelled (x) and time taken (y), if a car is not moving at a uniform speed
(c) Wages of a worker (x) and the number of hours of work (y)
(d) The number of students (x) and the fees paid by them (y)
(e) Number of rainy days (x) and the amount of rainfall on those days (y)
2. In which of the following is x in direct variation with y?

(a) x 5 8 9 11 (b) x 8 16 20 32 60
y 15 24 27 33 y 2 4 5 8 15

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