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The average height of 40 sticks is 154 cm. Some sticks of average height 160 cm are taken out. If the new average height is 150 cm, then how many sticks are remaining?

The average height of 40 sticks is 154 cm. Some sticks of average height 160 cm are taken out. If the new average height is 150 cm, then how many sticks are remaining? Correct Answer 24

Average of 40 sticks = (Sum of Length of 40 sticks) /40

⇒ 154 = (sum of length 40 sticks) /40

⇒ Sum of length 40 sticks = 6160

Let x sticks are taken out

Average of x sticks = (sum of length of x stick) /x

⇒ 160 = (sum of length of x sticks) /x

⇒ Sum of length of x sticks = 160x

Now, Remaining sticks = 40 - x

Average of (40 - x) sticks = {sum of length of (40 - x) stick} /(40 - x)

⇒ 150 = {sum of length of (40 - x) sticks} /(40 - x)

⇒ Sum of length of (40 - x) sticks = 150(40 - x) = 6000 - 150x

According to question,

⇒ 160x + 6000 - 150x = 6160

⇒ 10x = 160

⇒ x = 16

∴ Remaining sticks = 40 - x = 40 - 16 = 24

/40

⇒ 6160 = 160n - 150n + 6000

⇒ 10n = 160

⇒ n = 16

∴ Remaining sticks = 40 - n = 40 - 16 = 24

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