Average - Study Mode

[#231] The average of three consecutive odd numbers is 52 more than $${frac{1}{3}^{{ ext{rd}}}}$$ of the largest of these numbers. What is the smallest of these numbers?
Correct Answer

(D) 77

Explanation

Solution: Let the three consecutive odd numbers are $$eqalign{
& x,,x + 2,,x + 4 cr
& frac{{x + x + 2 + x + 4}}{3} = frac{1}{3}left( {x + 4}
ight) + 52 cr
& frac{{3x + 6}}{3} = frac{{x + 4 + 156}}{3} cr
& 3x + 6 = x + 4 + 156 cr
& 2x = 154 cr
& x = 77 cr} $$

[#232] The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the sixth and seventh numbers is:
Correct Answer

(B) 44.5

Explanation

Solution: Sum of 12 numbers = 12 × 39 = 468 Sum of last 5 numbers = 5 × 35 = 175 Sum of first 4 numbers = 4 × 40 = 160 [x08egin{array}{*{20}{c}}
{{5^{{ ext{th}}}}}&{{6^{{ ext{th}}}}}&{{7^{{ ext{th}}}}} \
{left( {x - 6}
ight)}&{left( x
ight)}&{left( {x - 11}
ight)}
end{array}] $$eqalign{
& 3x - 17 = 468 - left( {175 + 160}
ight) cr
& 3x = 133 + 17 cr
& x = 50 cr
& { ext{Average of }}{{ ext{6}}^{{ ext{th}}}}{ ext{ and }}{{ ext{7}}^{{ ext{th}}}}{ ext{ number}} cr
& = frac{{x + left( {x - 11}
ight)}}{2} cr
& = x - 5.5 cr
& = 50 - 5.5 cr
& = 44.5 cr} $$

[#233] Find the average of the first 20 multiples of 9.
Correct Answer

(B) 94.5

Explanation

Solution: First 20 multiple of 9 $$eqalign{
& { ext{Average}} = frac{{90 + 99}}{2} cr
& = 45 + 49.5 cr
& = 94.5{ ext{ Answer}} cr
& cr
& {x08f{Alternate ,Solution:}} cr
& { ext{Average}} = frac{{{ ext{First term}} + { ext{Last term}}}}{2} cr
& = frac{{9 + 180}}{2} cr
& = 4.5 + 90 cr
& = 94.5 cr} $$

[#234] Average temperature of a week is 30°C. If the average of first 4 days was 31°C, then average temperature of the remaining days will be:
Correct Answer

(D) 28.67°C

Explanation

Solution: Total temperature of the week = 30°C × 7 = 210°C Total temperature first four day = 31°C × 4 = 124°C Average temperature of remaining day $$eqalign{
& = frac{{{{210}^ circ }{ ext{C}} - {{124}^ circ }{ ext{C}}}}{3} cr
& = frac{{{{86}^ circ }{ ext{C}}}}{3} cr
& = {28.67^ circ }{ ext{C}} cr} $$

[#235] The average weight of a certain number of students in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weight of 80 kg join the group, the average weight of the students in the group decreases by 0.7 kg. The number of students initially in the group is:
Correct Answer

(B) 46

Explanation

Solution: Let the number of students = x Average of x students = 72 Total weight = 72x Change in weight = 10 × 78 - 4 × 80 = 460 Now, total students = x - 6 $$eqalign{
& { ext{Average}} = frac{{72x - 460}}{{x - 6}} cr
& 71.3 = frac{{72x - 460}}{{x - 6}} cr
& 0.7x = 32.2 cr
& x = 46 cr} $$