Average - Study Mode
[#61] Average of all even numbers between 104 and 148 is.
Correct Answer
(D) 126
Explanation
Solution: $$eqalign{
& { ext{Average}} = frac{{{ ext{First number}} + { ext{Last number}}}}{2} cr
& { ext{So,}} cr
& { ext{First number}} = 104 cr
& { ext{Last number}} = 148 cr
& { ext{Average}} = frac{{252}}{2} = 126 cr} $$ Alternate: Number of term between 104 and 148 146 = 106 + (n - 1)2 n = 21 Then, addition of all 21 term $$eqalign{
& = frac{{21}}{2}left[ {2 imes 106 + left( {21 - 1}
ight)2}
ight] cr
& = frac{{21}}{2}left[ {212 + 40}
ight] cr
& = frac{{21}}{2} imes 252 cr
& { ext{Average}} = frac{{21}}{2} imes frac{{252}}{{21}} = 126 cr} $$
[#62] In a one day match of 50 overs in an innings the team A had a run rate of 5.3 runs per over. Team B is playing and 5 overs are left and the required run rate to tie the match is 7.2 per over to match the score of team A. What is team B's score?
Correct Answer
(D) 229
Explanation
Solution: Run scored by team A $$ = frac{{50 imes 53}}{{10}} = 265{ ext{ runs}}$$ Run scored by team B in 5 over $$ = frac{{72}}{{10}} imes 5 = 36{ ext{ runs}}$$ Then, remaining run make by B = 265 - 36 = 229
[#63] 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:
Correct Answer
(B) $$xy$$
Explanation
Solution: $$eqalign{
& { ext{According to the question,}} cr
& { ext{Average of }}x{ ext{ number}} = {y^2} cr
& herefore { ext{Sum of }}x{ ext{ number}} = x{y^2} cr
& { ext{Average of }}y{ ext{ number}} = {x^2} cr
& herefore { ext{Sum of }}y{ ext{ number}} = y{x^2} cr
& { ext{Average of all number}} = frac{{x{y^2} + y{x^2}}}{{x + y}} cr
& = frac{{xyleft( {x + y}
ight)}}{{x + y}} cr
& = xy cr} $$
[#64] A student obtained the following marks in percentage in his semester examination English 50, Maths 65, Statistics 70, Economics 58 and Accountancy 63. The weights of these subjects are 2, 2, 1, 1 and 1 respectively. What is the weighted arithmetic mean?
Correct Answer
(A) 60
Explanation
Solution: Weighted arithmetic mean $$eqalign{
& = frac{{50 imes 2 + 65 imes 2 + 70 imes 1 + 58 imes 1 + 63 imes 1}}{{2 + 2 + 1 + 1 + 1}} cr
& = frac{{100 + 130 + 70 + 58 + 63}}{7} cr
& = frac{{421}}{7} cr
& = 60.14 approx 60 cr} $$
[#65] Visitor to a show were charged Rs. 15 each on the first day, Rs. 7.50 each on the second day and Rs. 2.50 each on the third day. The attendance on the three days was in the ratio 2 : 5 : 13. The average charge per person for the whole show was-
Correct Answer
(A) Rs. 5
Explanation
Solution: Let the attendance on the three days be 2x, 5x and 13x respectively. Then, total charges = Rs. (15 × 2x + 7.50 × 5x + 2.50 × 13x) = Rs. (30x + 37.5x + 32.5x) = Rs. 100x ∴ Average change per person = Rs. $$left( {frac{{100x}}{{2x + 5x + 13x}}}
ight)$$ = Rs. 5