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Direct anD inDirect Variations

Direct Variation indirect (inverse) Variation

If two quantities are associated in such a way that If two quantities a and b vary with each other
an increase in one quantity leads to a corresponding in such a manner that the product ab remains
increase in the other and vice versa, then such a constant and is positive, then we say that a and b
variation is called a direct variation. vary in indirect (inverse) variation.
4 7 In the following table, a and b vary inversely as
In the following table, a and b vary directly as = 8 × 32 = 16 × 16 and so on.
and so on. 12 21
a 4 7 21 28 a 8 16 32 256
b 12 21 63 84 b 32 16 8 1

applications of Direct and inverse Variations

time and Work Pipes and cisterns time and Distance
If a person can do a piece of A cistern or a water tank is The speed of a moving object
work in n days or hours, then connected with two types of is the distance covered by it in
unit time. If an object covers an
work done by the person in 1 pipes. One that fills it up is equal distance in equal interval
called an inlet; the other that
1
day or 1 hour is =    part of empties it is called an outlet. of time, then its speed is said to
be constant or uniform.
n

l If an inlet fills a tank in ‘n’ The distance travelled is directly
the work. hours, then the part of the proportional to the time and
1 tank filled in 1 hour is 1 . speed. For a given distance,
Conversely, if a person does time and speed are inversely
n n proportional.
part of the work in 1 day, then l If an outlet empties a tank The distance (d), speed (s), and
in ‘n’ hours, then the part of
he will complete the work in time taken (t) are connected by
the tank emptied in 1 hour the following relations:
n days. 1 d d
is − . s = or t = or d = s × t
n t s

Brain Sizzlers

1. 20 packets of detergent powder, each containing 1.5 kg cost `6000. What will be the price at this
rate of 15 packets each containing 3 kg?
2. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds
respectively, and they cross each other in 23 seconds. What would be the ratio of their speeds?
3. The floor plan drawing of a square and a rectangular room is drawn using the same scale. The plan shows
2
2
the area of the floor of the rectangular room as 12 cm for the actual area of 24 m . What is the area of the
floor of the square room in the plan if the actual side of the floor of the square room is 6 m?

295 Direct and Indirect Variations