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The average height of 45 sticks is 157 cm. Some sticks of average height 163 cm are taken out. If the new average height is 153 cm, then how many sticks are left?

The average height of 45 sticks is 157 cm. Some sticks of average height 163 cm are taken out. If the new average height is 153 cm, then how many sticks are left? Correct Answer 27

Given:

Average height of 45 sticks = 157 cm

New average height of the sticks after removing some sticks of height 163 cm = 153 cm

Formula used:

Average of n numbers = Sum of all the numbers/n

Calculation:

Total height of all the sticks initially = 45 × 157 = 7065

Let n number of sticks were removed

⇒ Total height of removed sticks = 163n

Also, according to the question:

Total height of remaining sticks = (45 - n)(153) = 6885 - 153n

Then, 7065 = 6885 - 153n + 163n

⇒ 180 = 10n

⇒ n = 18

∴ Remaining sticks = 45 - 18 = 27.

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