Average - Study Mode

[#141] The average weight of three boys A, B and C is $$frac{{163}}{3}$$ kg, while the average weight of three boys B, D and E is 53 kg. What is the average weight of A, B, C, D and E?
Correct Answer

(D) Data inadequate

Explanation

Solution: In this question, sum of numbers is provided, net required sum (i.e. A + B+ C+ D + E) cannot be calculated by the given data. Therefore the answer is Data inadequate.

[#142] Average of ten positive numbers is x. If each number is increased by 10%, then x :
Correct Answer

(D) is increased by 10%

Explanation

Solution: Let 10 numbers be x1, x2, x3, . . . . . . . x10 According to question average of these 10 numbers is 10 $$ Rightarrow frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}} = x$$ Now if each number is increased by 10%, then new average, say y. $$y = frac{{ {1.1x1 + 1.1x2 + 1.1x3 + .... + 1.1x10} }}{{10}}$$ $${kern 1pt} Rightarrow y = 1.1 imes {frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}}} $$ $$eqalign{
& Rightarrow y = 1.1x cr
& Rightarrow y,{ ext{is }}10\% ,{ ext{increased}} cr} $$

[#143] The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
Correct Answer

(C) Rs. 10, Rs. 16

Explanation

Solution: Total cost of 10 books = Rs. 120 Total cost of 8 books = Rs. 94 ⇒ The cost of 2 books = Rs. 26 Let the price of each book be x and y. ⇒ x + y = 26 - - - - - -(1) Given that the price of 1 book is 60% more than the other price $$eqalign{
& left( {frac{{160}}{{100}}}
ight)y + y = 26 cr
& Rightarrow yleft( {frac{{160}}{{100}} + 1}
ight) = 26 cr
& Rightarrow yleft( {frac{{160 + 100}}{{100}}}
ight) = 26 cr
& Rightarrow y = frac{{left( {26 imes 100}
ight)}}{{260}} cr
& Rightarrow y = 10 cr
& { ext{Substituting}},,y = 10,,{ ext{in }}{kern 1pt} left(1
ight){ ext{we get}}, cr
& x + 10 = 26 cr
& x = 16 cr} $$

[#144] The average age of 3 children in a family is 20% of the average age of the father and the eldest child. The total age of the mother and the youngest child is 39 years. If the father's age is 26 years, what is the age of the second child ?
Correct Answer

(D) Cannot be determined

Explanation

Solution: Since the total or average age of all the family members is not given, te given data is inadequate. So, the age of the second child cannot be determined.

[#145] Five years ago the average age of A, B, C, D was 45 years. By including X the present average of all the five is 49 years. Them the present age of X is-
Correct Answer

(B) 45 years

Explanation

Solution: Sum of the present ages of A, B, C and D = (45 × 4 + 5 × 4) years = 200 years Sum of the present ages of A, B, C, D and X = (49 × 5) years = 245 years ∴ X's present age = (245 - 200) years = 45 years