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Monday, 29 April 2019

MATHS SOLVED IN STEPS: Problems on Average - 05

37. The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then
A. None of these           B. x = y + z              C. 2x = y + z            D. x = 2y + 2z
Answer : Option C
Explanation :
Average of 6 numbers = x
=> Sum of 6 numbers = 6x
Average of the 3 numbers = y
=> Sum of these 3 numbers = 3y
Average of the remaining 3 numbers = z
=> Sum of the remaining 3 numbers = 3z
Now we know that 6x = 3y + 3z
=> 2x = y + z


38. The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. Find out the highest score of the player.
A. 150            B. 174             C. 180            D. 166
Answer : Option B
Explanation :
Total runs scored by the player in 40 innings = 40×50
Total runs scored by the player in 38 innings after excluding two innings= 38×48
Sum of the scores of the excluded innings = 40×50"38×48=2000"1824=176
Given that the scores of the excluded innings differ by 172. Hence let’s take the highest score as x + 172 and lowest score as x
Now x + 172 + x = 176
= > 2x = 4
= >x=4# 2=2
highest score as x + 172 = 2 + 172 = 174

39. The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, what is the average for the last four matches?
A. 34.25           B. 36.4           C. 40.2             D. 32.25
Answer : Option A
Explanation :
Total runs scored in 10 matches = 10×38.9
Total runs scored in first 6 matches = 6×42
Total runs scored in the last 4 matches = 10×38.9"6×42
Average of the runs scored in the last 4 matches
= (10×38.9"6×42)#4
= (389"252)#4
= 137#4=34.25


40. Suresh drives his car to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is his average speed for the whole journey ?
A. 32.5 km/hr.                        B. 35 km/hr
C. 37.5 km/hr                         D. 40 km/hr
Answer : Option C
Explanation :
If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,the average speed of the whole journey = 2xy/x+y kmph By using the same formula, we can find out the average speed quicklyaverage speed = ( 2×50×30)#(50+30)
= (2×50×30)#80
= (2×50×3) # 8
= (50×3)#4
=(25×3)# 2=75#2=37.5

41. The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. What is the average
age of the family?
 A. 21 years        B. 20 years          C. 18 years              D. 19 years
Answer : Option D
Explanation :
Total of the age of husband and wife = 2×23=46
Total of the age of husband and wife after 5 years
+ Age of the 1 year old child =46+5+5+1=57
Average age of the family=57#3=19

42. In an examination, a student’s average marks were 63. If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65. How many subjects were there in the examination?
A. 12          B. 11            C. 13               D. 14
Answer : Option B
Explanation :
Let the number of subjects = x
Then, Total marks he scored for all subjects = 63x
If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65
=> Total marks he would have scored for all subjects = 65x
Now we can form the equation as 65x - 63x = the
additional marks of the student = 20 + 2 = 22
=> 2x = 22
=>    x=  22#2
           =11


43. The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. How many workers are there in the workshop ?
A. 21             B. 22             C. 23                    D.24
Answer: Option A
Explanation:
Let the number of workers = x
Given that average
salary of all the workers = Rs.8000
then total salary of all workers = 8000x
Given that average salary of 7 technicians is Rs.12000
=>
Total salary of 7 technicians = 7×12000=84000
Number of the rest of the employees = (x - 7)
Average salary of the rest of the employees = Rs.6000
Total salary of the rest of the employees = (x - 7)(6000) 8000x = 84000 + (x - 7)(6000)
= > 8x = 84 + (x - 7)(6)
= > 8x = 84 + 6x - 42
= > 2x = 42
= >x=21
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Age 
* MATHS (SOLVED IN STEPS ==> Pipe and Cisterns
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK



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