Average - Study Mode

[#176] Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 49 yr. How old is E?
Correct Answer

(C) 45 years

Explanation

Solution: Total present age of A, B, C and D = (45 × 4) + (4 × 5) = 200 years Total age present age of A, B, C, D and E = 49 × 5 = 245 years So, Age of E = 45 years

[#177] Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.
Correct Answer

(C) 93

Explanation

Solution: Total of 80 numbers = 80 × 42 = 3360 Now, total of 85 numbers = 85 × 45 = 3825 Hence, sum of 5 numbers = 3825 - 3360 = 465 Average of five numbers = $$frac{{465}}{5}$$ = 93 Alternatively, Solve while reading method: Average of 80 number was 42 When 5 more numbers are added average become 45 that means 3 is given to each number to make their average. 45 and 5 numbers also keep 45 as to maintain the entire average. So, the sum of five numbers = 240 + 225 = 465 Hence, average of five numbers = 93

[#178] Find the average increase rate, if increase in the population in the first year is 30% and that in the second year is 40%.
Correct Answer

(A) 41%

Explanation

Solution: Let 100 be the original population. 1 st year's population increased = 30% So, Population after first year = (100 + 30% of 100) = 130 Population in second year increases by 40%, Then Population = (130 + 40% of 130) = 182 The final population become 182 which was originally at 100. It means there is 82% increment in the population in 2 years So, Average increment = $$frac{{82}}{2}$$ = 41% Mind Calculation Method: Increase in population is given by, 100 == 30% $$ uparrow $$ ⇒ 130 == 40% $$ uparrow $$ ⇒ 182 Hence, average increase = $$frac{{82}}{2}$$ = 41%

[#179] One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
Correct Answer

(C) $$frac{{1800}}{{53}}$$ km/h

Explanation

Solution: Let distance be 120 km
Hence 30 km is covered by @25 kmph and 40 km covered by @30 kmph and rest 50 km has been covered @50 kmph Now, $$eqalign{
& { ext{average}} = {frac{{120}}{{{ ext{total}},{ ext{time}},{ ext{taken}}}}} cr
& = frac{{120}}{{frac{{30}}{{25}} + frac{{40}}{{30}} + frac{{50}}{{50}}}} cr
& = frac{{3600}}{{106}} cr
& = frac{{1800}}{{53}},{ ext{km/h}} cr} $$

[#180] A batsman makes a score of 270 runs in the 87 th inning and thus increase his average by a certain number of runs that is a whole number. Find the possible values of the new average.
Correct Answer

(D) All of these

Explanation

Solution: Part of the runs scored in the 87 th innings will go towards increasing the average of the first 86 innings to the new average and remaining part of the runs will go towards maintaining the new average for the 87 th innings. The only constraint in this problem is that there is increase in average by a whole number of runs. This is possible for all three options.