Average - Study Mode

[#226] A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.
Correct Answer

(D) [23frac{{23}}{{59}}] km

Explanation

Solution: $$eqalign{
& { ext{Average}},{ ext{speed}} cr
& = frac{{{ ext{total}},{ ext{distance}},{ ext{covered}}}}{{{ ext{total}},{ ext{time}}}} cr
& { ext{Total}},{ ext{Distance}} cr
& = {16 + 20 + 10} cr
& = 46,{ ext{km}} cr
& { ext{Time}},{ ext{taken}} cr
& = {frac{{16}}{{20}}} + {frac{{20}}{{40}}} + {frac{{10}}{{15}}} cr
& = {frac{{4}}{{5}}} + {frac{{1}}{{2}}} + {frac{{2}}{{3}}} cr
& = {frac{{24 + 15 + 20}}{{30}}} cr
& = frac{{59}}{{30}} cr
& { ext{Average}},{ ext{speed}} cr
& = frac{{46 imes 30}}{{59}} cr
& = 23frac{{23}}{{59}},{ ext{km/hr}} cr} $$

[#227] The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8 kg, 70.3 kg and 66.7 kg join the
class, then the average weight of all the students increases by 300 g. The number of students in the class, initially, is:
Correct Answer

(B) 16

Explanation

Solution: $$eqalign{
& { ext{Let total students}} = x cr
& frac{{68.5x + 280}}{{x + 4}} = 68.8 cr
& 68.5x + 280 = 68.8x + 275.2 cr
& 0.3x = 4.8 cr
& x = 16 cr} $$

[#228] Average age of 20 student is 21 years. 2 students leave the group and 1 new student joins the group. The average now becomes 20 years. If age of one of the student who left the group is 26 years and the one who joined is 20 years, then what is the age (in years) of other student who left the group?
Correct Answer

(B) 34

Explanation

Solution: Average age of 20 students = 21 years Total age of 20 students = 21 × 20 = 420 2 students leave and one student come in group. Total age of 19 students = 19 × 20 = 380 years Student left 420 - A - B + N = 380 26 + B - 20 = 40 B = 40 - 6 = 34 years

[#229] The average of n number is 45. If 60% of the number are increased by 5 each and the remaining numbers are decreased by 10 each, then what is the average of the number so obtained?
Correct Answer

(C) 44

Explanation

Solution: $$eqalign{
& { ext{Average of }}n{ ext{ numbers}} = 45 cr
& { ext{Let, }}n = 100 cr
& { ext{New average}} cr
& = frac{{100 imes 45 + 60 imes 5 - 40 imes 10}}{{100}} cr
& = frac{{100 imes 45}}{{100}} + frac{{300 - 400}}{{100}} cr
& = 45 - 1 cr
& = 44 cr} $$

[#230] Rita buys 5 sarees at an average cost of Rs. 2250. If she buys three more at an average cost of Rs. 2750, what will be the average (in Rs.) of all the sarees she buys?
Correct Answer

(A) 2437.5

Explanation

Solution: $$eqalign{
& { ext{Average of all the sarees}} cr
& = frac{{2250 imes 5 + 2750 imes 3}}{8} cr
& = frac{{11250 + 8250}}{8} cr
& = frac{{19500}}{8} cr
& { ext{Average of all the sarees}} = 2437.5 cr} $$