model 1 basic average questions Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [S.S.C. (CHSL) 2011]

The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is

a) $\text"x+y"/\text"2xy"$

b) $\text"2xy"/\text"x+y"$

c) $(x^2+y^2)/\text"x+y"$

d) $\text"xy"/\text"x+y"$

Answer: (b)

Sum of x numbers = xy

Sum of y numbers = xy

∴ Required average = ${xy+xy}/{x+y}$ = ${2xy}/{x+y}$

Aliter : Using Rule 10,

Here, $n_1$ = x, $a_1$ = y

$n_2$ = y, $a_2$ = x

∴ Average = ${n_1a_1+n_2a_2}/{n_1+n_2}$

= ${xy+yx}/{x+y}$ = ${2xy}/{x+y}$

Question : 2 [S.S.C. (CISF) 2011]

If average of 20 observations x1,x2, ....., x20 is y, then the average of x1 – 101, x2 – 101, x3 –101, ....., x20 –101 is

a) y-20

b) y-101

c) 20y

d) 101y

Answer: (b)

${X_1 + X_2 + X_3 + X_4 + ..... + X_20}/20 = Y$

$X_1 + X_2 + X_3 + X_4 + ..... + X_20 = 20Y$

$= {X_1 - 101 + X_2 - 101 + X_3 - 101 + X_4 - 101 + ..... + X_20 - 101}/20$

$= (X_1 + X_2 + X_3 + X_4 + ..... + X_20) - 20 x 101/20$

$\text"20Y - 20 x 101"/20$

= Y - 101

Question : 3 [S.S.C. (CHSL) 2011]

The average of $x$ numbers is $y^2$ and the average of $y$ numbers is $x^2$. So the average of all the numbers taken together is

a) $(x^3+y^3)/\text"x+y"$

b) $xy$

c) $(x^2+y^2)/\text"x+y"$

d) $xy^2+yx^2$

Answer: (b)

According to the question,

Average of x number is y2

∴ Sum of x number is = xy2

Average of y number is = x2

∴ Sum of y number is = yx2

Average of all number is

= ${xy^2+yx^2}/{x+y}$

= ${xy(x+y)}/{x+y}$

= xy

Question : 4 [S.S.C. (CGL) 2016]

In a class, average height of all students is ‘a’ cms. Among them, average height of 10 students is ‘b’ cms and the average height of the remaining students is ‘c’ cms. Find the number of students in the class. (Here a > c and b > c )

a) $(a(b-c))/(a-c)$

b) $(b-c)/(a-c)$

c) $(b-c)/\text"10(a-c)"$

d) $\text"10(b-c)"/(a-c)$

Answer: (d)

Let the total number of students in the class be n.

According to the question,

an = 10 × b + (n – 10) c

⇒ an = 10b + nc – 10c

⇒ an – cn = 10b – 10c

⇒ n (a – c) = 10 (b – c)

$⇒ n =\text"10 (b - c )"/ ( a - c )$

Question : 5 [S.S.C. (CGL) 2015]

Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new numbers is

a) $a+(2^(n-1)-1)/n$

b) $a+2(2^n-1)/n$

c) $a+2^(n-1)/n$

d) $a+(2^n-1)/n$

Answer: (b)

Sum of new numbers

= na + (2 + 4 + 8 + 16 ..... to n terms)

Now, S = 2 + 4 + 8 + 16 + ..... to n terms

Here, a = first term = 2

r = common ratio = $4/2$ = 2

It is a geometric series.

∴ S =${a({r^n} - 1)}/{r-1}$= ${2({2^n} - 1)}/{2-1}$

= 2 ($2^n$ –1)

∴ Required average

= ${na +2({2^n}-1)}/n$

a +${2({2^n}-1)}/n$

IMPORTANT quantitative aptitude EXERCISES

Recently Added Subject & Categories For All Competitive Exams

Top 149+ Biology General Knowledge Practice MCQ Test

Top Biology Ecology & Environment Awareness General Knowledge Multiple Choice Questions And Answers. General Science GK Practice Test For Competitive Exams

December-16-2022 by Careericons

Continue Reading »

Important General Science Biology Practice MCQ Questions

Top General Science Biology In Human Welfare Based Multiple Choice Questions And Answers, Practice MCQ Test For All Competitive Exams, NEET, SSC, Interview

December-06-2022 by Careericons

Continue Reading »

Top 199+ General Science Biology Practice Test, MCQ PDF

Most Important General Science Biology Human Welfare Multiple Choice Questions And Answers (MCQ) PDF, Practice Test For All Competitive Exams, SSC, NEET, RRB

December-01-2022 by Careericons

Continue Reading »

New General Science Biology MCQ Online Practice Test, PDF

Top Most General Science Biology Food Production Multiple Choice Questions And Answers (MCQ), Online GK Practice Test, PDF For All Competitive Exams, NEET

November-29-2022 by Careericons

Continue Reading »