Average - Study Mode

[#211] The average age of 30 students is 9 years. If the age of their teacher is included, the average age becomes 10 years. The age of the teacher (in years) is :
Correct Answer

(D) 40

Explanation

Solution: Let the age of teacher = x years According to the question, 30 × 9 + x = 31 × 10 270 + x = 310 x = 40 years

[#212] The average age of 20 boys in a class is 12 years. 5 new boys are admitted to the class whose average age is 7 years. The average age of all the boys in the class becomes:
Correct Answer

(D) 11 years

Explanation

Solution: According to the question, Average = $$frac{20 × 12 + 5 × 7}{25}$$ =
$$frac{240 + 35}{25}$$ =
$$frac{275}{25}$$ = 11 years

[#213] The frequency distribution data is given below. If the average age is 17 years, the value of m is Age (in years) : 8 20 26 29 No. of people : 3 2 m 1
Correct Answer

(A) 1

Explanation

Solution: According to the question, Age (in year) : 8 20 26 29 No. of people : ↓×3 +↓×2 +↓×m +↓×1 = 6 + m Total : 24 +40 +26m +29 = 93 + 26m Average = $$frac{93 + 26m}{6 + m}$$ xa0 = 17 ⇒ 93 + 26m = 102 + 17m ⇒ 9m = 9 ⇒ m = 1

[#214] The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. The average of the remaining two numbers is :
Correct Answer

(A) 4.6

Explanation

Solution: Let the six number be a, b, c, d, e, f According to the question, ⇒
$$frac{a + b + c + d + e + f}{6}$$ xa0 xa0 = 3.95 ⇒ a + b + c + d + e + f = 23.7.....(i) $$frac{a + b}{2}$$xa0 = 3.4 ⇒ a + b = 6.8.....(ii) $$frac{c + d}{2}$$xa0 = 3.85 ⇒ c + d = 7.7.....(iii) Put the value of equation (ii) and equation (iii) in equation (i) e + f = 23.7 - 7.7 - 6.8 e + f = 9.2 ∴ Average =$$frac{9.2}{2}$$ = 4.6

[#215] If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value of x is :
Correct Answer

(D) 16

Explanation

Solution: Arithmetic mean $$frac{{{ ext{Total sum}}}}{{{ ext{Total number}}}}$$ According to the question, ⇒ 10 = $$frac{7 + 5 + 13 + x + 9}{5}$$ ⇒ 50 = x + 34 ⇒ x = 50 - 34 ⇒ x = 16