Average - Study Mode

[#246] The average height of 35 girls in a class was calculated as 160 cm. It was later found that the height of one of the girls in the class was wrongly written as 144 cm, whereas her actual height was 104 cm. What is the actual average height of the girls in the class? ( rounded off to 2 digits after decimal)-
Correct Answer

158.54 cm

Explanation

Solution: Correct sum = (160 × 35 + 104 - 144) cm = 5560 cm ∴ Actual average height = $$left( {frac{{5560}}{{35}}}
ight)$$ xa0cm = 158.857 cm $$ approx $$ 158.86 cm

[#247] The average of the two-digit numbers, which remain the same when the digits interchange their positions, is-
Correct Answer

(C) 55

Explanation

Solution: Average $$ = frac{{11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99}}{9}$$ $$ = frac{{left( {11 + 99}
ight) + left( {22 + 88}
ight) + left( {33 + 77}
ight) + left( {44 + 66}
ight) + 55}}{9}$$ $$eqalign{
& = frac{{4 imes 110 + 55}}{9} cr
& = frac{{495}}{9} cr
& = 55 cr} $$

[#248] The average of a non-zero number and its square is 5 times the number. The number is-
Correct Answer

(A) 9

Explanation

Solution: Let the number be x Then, $$eqalign{
& Rightarrow frac{{x + {x^2}}}{2} = 5x cr
& Rightarrow {x^2} - 9x = 0 cr
& Rightarrow xleft( {x - 9}
ight) = 0 cr
& Rightarrow x = 0{ ext{ or }}x = 9 cr} $$ So, the number is 9

[#249] The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age of 33 years are replaced by 3 youngsters. The average age of the new comers is :
Correct Answer

(C) 22 years

Explanation

Solution: According to the question, Increased age of 11 players = 11 × 3 = 33 years Current age of 3 players who are replaced = 3 × 33 = 99 years ∴ Age of 3 newcomers = 99 - 33 = 66 years ∴ Average age = $$frac{66}{3}$$ xa0= 22 years

[#250] The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is ?
Correct Answer

(D) 35

Explanation

Solution: Sum of five number = 27 × 5 = 135 Sum of four number = 25 × 4 = 100 Excluded number = 135 - 100 = 35