Average - Study Mode

[#351] A certain factory employed 600 men and 400 women and the average wage was Rs. 25.50 per day. If women got Rs. 5 less than a man, then what are their daily wages?
Correct Answer

(B) Man: Rs. 27.50, Woman: Rs. 22.50

Explanation

Solution: Let the daily wage of a man be Rs. x Then, daily wage of a woman = Rs. (x - 5) Now, ⇒ 600x + 400(x - 5) = 25.50 × (600 + 400) ⇒ 1000x = 27500 ⇒ x = 27.50 ∴ Man's daily wages = Rs. 27.50 Woman's daily wages = (x - 5) = Rs. 22.50

[#352] A coaching institute has students in 3 batches – X, Y and Z. In a certain examination, the average marks obtained by these batches are 72, 60 and 50 respectively. The average marks of batches X and Y taken together is 69. If the ratio of the number of students in batches Y and Z is 6 : 7. What is the average score of all the three batches put together?
Correct Answer

(D) 64.7

Explanation

Solution: Let the number of students in batches Y and Z be 6x and 7x respectively, and the number of students in batch X be y. Then, $$eqalign{
& Rightarrow 72y + 60 imes 6x = 69left( {6x + y}
ight) cr
& Rightarrow 72y + 360x = 414x + 69y cr
& Rightarrow 3y = 54x cr
& Rightarrow y = 18x cr} $$ ∴ Required average $$eqalign{
& = frac{{72 imes 18x + 60 imes 6x + 50 imes 7x}}{{18x + 6x + 7x}} cr
& = frac{{1296 + 360 + 350}}{{31}} cr
& = frac{{2006}}{{31}} cr
& = 64.7 cr} $$

[#353] In an engineering college the average salary of all engineering graduates from Mechanical trade is Rs. 2.45 lacs per annum and that of the engineering graduates from Electronics trade is Rs. 3.56 lacs per annum. The average salary of all Mechanical and Electronics graduates is Rs. 3.12 lacs per annum. Find the least number of Electronics graduates passing out from this institute.-
Correct Answer

(C) 67

Explanation

Solution: Let the number of Mechanical Engineering graduates be M and the number of Electronics Engineering graduates be E. Then, $$ Rightarrow 2.45M + 3.56E = $$ xa0 xa0$$3.12left( {M + E}
ight)$$ $$ Rightarrow 2.45M + 3.56E = $$ xa0 xa0$$3.12M + 3.12E$$ $$eqalign{
& Rightarrow 0.44E = 0.67M cr
& Rightarrow frac{M}{E} = frac{{0.44}}{{0.67}} = frac{{44}}{{67}} cr} $$ Since the ratio 44 : 67 is in its simplest form, So least number of Electronics graduates = 67

[#354] 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 price of the two books = Rs. [(12 × 10) - (11.75 × 8)] = Rs. (120 - 94) = Rs. 26 Let the price of one book be Rs. x Then, the price of other book = Rs. (x + 60 % of x) = Rs. $$left( {x + frac{3}{5}x}
ight)$$ = Rs. $$left( { frac{8x}{5}}
ight)$$ So, $${x + frac{8x}{5}}$$ xa0 = 26 ⇒ 13x = 130 ⇒ x = 10

[#355] 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
Correct Answer

(B) $$77frac{2}{3}$$

Explanation

Solution: Required average $$eqalign{
& = frac{{left( {76 imes 16}
ight) - left( {75 imes 10}
ight)}}{6} cr
& = left( {frac{{1216 - 750}}{6}}
ight) cr
& = frac{{466}}{6} cr
& = frac{{233}}{3} cr
& = 77frac{2}{3} cr} $$