Average - Study Mode
[#1] Mean of 10 numbers is 30. Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32. The correct mean is :
Correct Answer
(A) 25.5
Explanation
Solution: According to the question, Mean of 10 numbers is = 30 ∴ Sum of 10 numbers is = 300 It was observed that numbers 15, 23 are wrongly taken as 51, 32 Difference = (51 + 32) - (15 + 23) = 83 - 38 = 45 (more) ∴ Actual sum of 10 numbers = 300 - 45 = 255 ∴ Actual average of 10 numbers = $$frac{255}{10}$$ = 25.5
[#2] The average age of a family of 10 members is 20 years. If the age of the youngest member of the family is 10 years, then the average age of the members of the family just before the birth of the youngest member was approximately.
Correct Answer
(D) $$11frac{1}{9}$$ years
(H) $$11frac{1}{9}$$ years
Explanation
Solution: According to the question, Average age of a family of 10 members is = 20 years Sum of the age of 10 members = 20 × 10 = 200 years If the age of youngest member is = 10 years Sum of the age of 9 members at the time of birth of youngest member = 200 - 10 × 10 = 200 - 100 = 100 years ∴ Average of 9 members is = $$frac{100}{9}$$ = $$11frac{1}{9}$$ years
[#3] a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. The average of all the numbers is :
Correct Answer
(B) $$left( {frac{{1 + d}}{2}}
ight)$$
Explanation
Solution: According to the question, Consecutive even numbers = a, b, c, d, e, f, g Consecutive odd numbers = j, k, l, m, n Consecutive even numbers 2, 4, 6, 8 , 10, 12, 14 $$frac{2 + 4 + 6 + 8 + 10 + 12 + 14}{7}$$ = $$frac{56}{7}$$ = 8 middle term Consecutive odd numbers 1, 3, 5 , 7, 9 $$frac{1 + 3 + 5 + 7 + 9}{2}$$ = $$frac{25}{5}$$ = 5 middle term ∴ Same as in above situation. Average of even numbers = d Average of odd numbers = 1 ∴ Average of all numbers = $$frac{1 + d}{2}$$
[#4] Out of four numbers the average of the first three is 16 and that of the last three is 15. If the last number is 20, than first number is :
Correct Answer
(C) 23
Explanation
Solution: Let a, b, c, d are four number ∵ Average of first three number a, b, c = 16 Total of (a + b + c) = 16 × 3 = 48.....(i) Again ∴ Average of last 3 numbers b, c, d = 15 ⇒ Total of (b + c + d) = 15 × 3 = 45.....(ii) ⇒ Subtracting equation (i) - (ii), we get ⇒ (a + b + c) - (b + c + d) = 48 - 45 ⇒ a - d = 3 ⇒ a = - 20 = 3 [Given d = 20] ⇒ a = 23 ⇒ Therefore, first number a = 23
[#5] Mukesh has twice as much money as Soham. Soham has 50% more money than Pankaj. If the average money with them is Rs. 110, then Mukesh has :
Correct Answer
(C) Rs. 180
Explanation
Solution: M : S : P 2 ×3 : 1 ×3 3 : 2 6 : 3 : 2 = 11 Average = $$frac{11}{3}$$ unit Average = $$frac{11}{3}$$ unit = Rs. 110 1 unit = 10 × 3 = Rs. 30 ∴ Mukesh has = 6 unit = 6 × 30 = Rs. 180