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SOLUTION

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