Average - Study Mode

[#171] A man purchased 7 bags of rice at the rate of Rs. 800 each, 8 bags of rice at Rs. 1000 each and 5 bags of rice at the rate of Rs. 1200 each. What is the average cost of one bag of rice ?
Correct Answer

(B) Rs. 980

Explanation

Solution: According to the question, Average = $$frac{7 × 800 + 8 × 1000 + 5 × 1200}{20}$$ = $$frac{5600 + 8000 + 6000}{20}$$ = $$frac{19600}{20}$$ ∴ Average = Rs. 980

[#172] The average of 30 numbers is 40 and that of other 40 numbers is 30. The average of all the numbers is :
Correct Answer

(A) $$34frac{2}{7}$$

Explanation

Solution: According to the question, Average of 30 numbers is = 40 Sum of 30 numbers is = 40 × 30 = 1200 Average of 40 numbers is = 30 Sum of 40 numbers is = 40
× 30 = 1200 Total average = $$frac{1200 + 1200}{70}$$ = $$frac{2400}{70}$$ = $$34frac{2}{7}$$

[#173] The average marks of four subjects is 120. If 33 was misread as 13 during the calculation, what will be the correct average?
Correct Answer

(C) 125

Explanation

Solution: $$eqalign{
& { ext{Correct average}} cr
& = 120 + left( {frac{{33 - 13}}{4}}
ight) cr
& = 120 + 5 cr
& = 125 cr} $$ Solve while reading method: Average given is 120. Difference of 33 and 13 is 20. That means 20 must be added to total. Then average of is and so must be added to average, i.e. Correct average = 120 + 5 = 125

[#174] Students of three different classes appeared in common examination. Pass average of 10 students of first class was 70%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
Correct Answer

(D) 72%

Explanation

Solution: $$eqalign{
& { ext{Sum}},{ ext{of}},{ ext{pass}},{ ext{student}},{ ext{}},{ ext{first,}},{ ext{second}},{ ext{and}},{ ext{third}},{ ext{class}}, cr
& = left( {70\% ,{ ext{of}},10}
ight) + left( {60\% ,{ ext{of}},15}
ight) + left( {80\% ,{ ext{of}},25}
ight) cr
& = 7 + 9 + 20 = 36 cr
& { ext{Total}},{ ext{students}},{ ext{appeared}}, cr
& = 10 + 15 + 25 = 50 cr
& { ext{Pass}},{ ext{average}}, cr
& = 36 imes frac{{100}}{{50}} = 72\% cr} $$

[#175] A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.
Correct Answer

(A) 24

Explanation

Solution: Required average speed, $$ = {frac{{left( {3 imes 40 imes 30 imes 15}
ight)}}{{ {left( {40 imes 30}
ight) + left( {40 imes 15}
ight) + left( {30 imes 15}
ight)} }}} $$ $$ = 24,{ ext{km/hr}}$$ Alternatively Time taken to traveled $$frac{1}{3}$$ distance of journey with speed 40 kmph, $$ = frac{{ {frac{1}{3}} }}{{40}} = frac{1}{{120}}$$ Time taken to traveled $$frac{1}{3}$$ distance of journey with speed 30 kmph, $$ = frac{{ {frac{1}{3}} }}{{30}} = frac{1}{{90}}$$ Time taken to traveled $$frac{1}{3}$$ distance of journey with speed 15 kmph, $$eqalign{
& = frac{{ {frac{1}{3}} }}{{15}} = frac{1}{{45}} cr
& { ext{Total time taken}} cr
& = {frac{1}{{120}}} + {frac{1}{{90}}} + {frac{1}{{45}}} cr
& = frac{{45}}{{1080}} cr
& { ext{Average speed}} cr
& = frac{{{ ext{Total distance traveled}}}}{{{ ext{Total time taken}}}} cr
& = frac{1}{{ {frac{{45}}{{1080}}} }} cr
& = 24,{ ext{kmph}} cr} $$