Question

The average of 16 numbers is 68.5 If two numbers 54 and 37 are replaced by 45 and 73 and one more number x is excluded, then the average of the numbers decreases by 1.5. The value of x is:

• A. 111
• B. 109
• C. 118
• D. 120

Answer 1

Answer:

C. 118

Solution : Average × Number = Sum ⇒ 68.5 × 16 = 1096 According to question Then, 54 + 37 = 91 and 45 + 73 = 118 91 replaced by 118 So, 118 - 91 = 27 and ⇒ 1096 + 27 = 1123 and after that x excluded New Sum = 1123-x ---(i) New average is 68.5 - 1.5 = 67 ⇒ 67 × 15( number) = 1005 ( new sum) ---(ii) From (i) & (ii) equal ⇒ 1005 = 1123 - x ⇒ x = 118 Alternate Method : Given: Average of 16 numbers is 68.5 54 and 37 are replaced by 45 and 73 Concept Used: Average = Sum of all observations/Total number of observations Calculation: Sum of all observations = Average × Total number of observations ⇒ Sum of all observations = 68.5 × 16 ⇒ Sum of all observations = 1096 54 and 37 are replaced by 45 and 73 ⇒ 54 + 37 = 91 replaced by 45 + 73 = 118 91 is replaced by 118, and one more number, i.e. x is excluded ⇒ 118 – 91 = 27 is added to the total sum and x is excluded New Sum = 1096 + 27 – x ⇒ New Sum = 1123 – x, The average is decreased by 1.5 New average = 68.5 – 1.5 ⇒ New average = 67 Total numbers = 16 – 1 ⇒ Total numbers = 15 New sum of all observations = 67 × 15 ⇒ New sum of all observations = 1005 ⇒ x = New Sum –Sum ⇒ x = 1123 – 1005 ⇒ x = 118 ∴ The value of x is 118.