Average, General Mathematics

Question: A cricketer has a certain average for `9` innings. In the tenth inning, he scores `100` runs ,thereby increasing his average by `8` runs. His new average is :
A
`20 runs`

B
`24 runs`

C
`28 runs`

D
`32 runs`

Note: Let average for `9` innings be x. Then, `(9x + 100)/10` `= x + 8 ⇒ 10x + 80` `= 9x + 100 ⇒ x = 20`. :. New average `= (x + 8)` `= 28 runs`.
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Question: A man whose bowling average is `12.4` takes `5` wickets for `26` runs and thereby decreases his average by `0.4`.The number of wickets, taken by him before his last match is :
A
`85`

B
`78`

C
`72`

D
`64`

Note: Let the number of wickets taken before the last match be x. Then, `(12.4x + 26)/(x + 5)` `= 12 ⇒ 12.4x + 26` `= 12x + 60` ` ⇒ 0 .4x ` `= 34 ⇒ x = 34/0.4` `= 340/4` `= 85`
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Question: The mean temperature of Monday to Wednesday was `37∘C and of Tuesday to Thursday was `34∘C.If the temperature on Thursday was `4/5 th`that of Monday ,the temperature on Thursday was:
A
`36.5^0 C`

B
`36^0 C``

C
`35.^0 C`

D
`34^0 C`

Note: M + T + W `= (3 xx 37)` `= 111, T + W + Th` `= (3 xx 34)` `= 102` `Now ,Th = 4/5 M ⇒ M = 5/4 Th`. (M + T + W) - (T + W + Th) `= 9 ⇒ M - Th = 9 `⇒ (5/4 Th - Th = 9)` `or Th = 36`
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Question: The average weight of `3` men A ,B and C is `84 kg`.Another man D joins the group and the average now becomes `80 kg`.If another man E,whose weight is `3 kg`more than that of D,replaces .A then the average weight of B,C,D and E becomes `79 kg`.The weight of A is :
A
`70 kg`

B
`72 kg`

C
`75 kg`

D
`80 kg`

Note: A + B + C `= (84 xx 3)` `= 252 kg`, A + B + C + D `= (80 xx 4)` `= 320 kg` `:. D = (320 - 252) kg` `= 68 kg, E = (68 + 3) kg` `= 71 kg` B + C + D + E `= 316 kg` Now (A + B + C + D) - (B + C + D + E) `= (320 - 316) kg` `= 4 kg` `:. A - E = 4 ⇒ A ⇒ A` `= (4 + E)` `= 75 kg`.
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Question: A team of `8` person joins in a shooting compertition. The best marksman scored `85`points.If he had scored `92`points ,the average score for the team would have been `84`.The number of points ,the team scored, was :
A
`672`

B
`665`

C
`645`

D
`588`

Note: Let the total score be x. `:. (x + 92 - 85)/8` `= 84 ⇒ x + 7 ` `= 672 ⇒ x = 665`.
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Question: Three years ago, the average age of A ,B and C was `27` year and that of B and C, `5` years .A ,s present age is :
A
`30 yrs`

B
`35 yrs`

C
`40 yrs`

D
`48 yrs`

Note: present ago of ( A + B + C) `= (27 xx 3 + 3 xx 3)` `= 90 years` present ago of (B + C) `= (20 xx 2 + 2 xx 5)` `= 50 years` `:. A,s present age `= (90 - 50) years` `= 40 years`
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Question: Three years ago, the average age of a family of `5` members was `17` years .A baby having been born ,the average age of the family is the same today. The present age of the baby is :
A
`2 yrs`

B
`2.4 yrs`

C
`3 yrs`

D
`1.5 yrs`

Note: Total age of `5` members, `3` years ago `= (17 xx 5)` Total age of `5`members now `= (85 + 3 xx 5)` `= 100 years` Total age of members now `= (17 xx 6)` `= 102 years` Age of the baby `= 2 years`
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Question: Five years ago, the average age of A,B,C and D was `45` years .With E joing them now, the average of all the five is `49`.How old is E ?
A
`25 yrs`

B
`40 yrs`

C
`45 yrs`

D
`64 yrs

Note: (A + B + C + D),five years ago `= (45 xx 4)` `= 180 years` (A + B + C + D), now `= (180 + 5 xx 4) years` `= 200 years` A + B + C + D + E, now `= (49 xx 5) years` `= 245 years` :. E, now `= (245 - 200)` `= 45 years`
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Question: Five years ago, The average age of Q was `15` years. A average age of P,Q and R today is `20` years. How old will R be after `10` years ?
A
`35 years`

B
`40 years`

C
`30 years`

D
`50 years`

Note: (P + Q),five years ago `= (15 xx 2)` `= 30 years` (P + Q), now `= (30 + xx 2) years` `= 40 years` (P + Q + R),now `= (20 xx 3) years` `= 60 years` :. R now `= (60 - 40) years` `= 20 years` R, after `10` years `= (20 + 10) years` `= 30 years`
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Question: The average age of boys in the class is twice the number of girls in the class.If the ratio of boys and girls in the class of `36` be `5 : 1`,what is the total of the ages (in years) of the boys in the class ?
A
`490`

B
`196`

C
`420`

D
`360`

Note: Number of boys `= (36 xx 5/6) = 30` Number of girls `= 6` A average age of boys `= (2 xx 6) = 12 years` :. Total age of boys `= (30 xx 12) years` `= 360 years`
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Question: A cricketer has a certain average for `9` innings. In the tenth inning, he scores `100` runs ,thereby increasing his average by `8` runs. His new average is :

Question: A man whose bowling average is `12.4` takes `5` wickets for `26` runs and thereby decreases his average by `0.4`.The number of wickets, taken by him before his last match is :

Question: The mean temperature of Monday to Wednesday was `37∘C and of Tuesday to Thursday was `34∘C.If the temperature on Thursday was `4/5 th`that of Monday ,the temperature on Thursday was:

Question: The average weight of `3` men A ,B and C is `84 kg`.Another man D joins the group and the average now becomes `80 kg`.If another man E,whose weight is `3 kg`more than that of D,replaces .A then the average weight of B,C,D and E becomes `79 kg`.The weight of A is :

Question: A team of `8` person joins in a shooting compertition. The best marksman scored `85`points.If he had scored `92`points ,the average score for the team would have been `84`.The number of points ,the team scored, was :

Question: Three years ago, the average age of A ,B and C was `27` year and that of B and C, `5` years .A ,s present age is :

Question: Three years ago, the average age of a family of `5` members was `17` years .A baby having been born ,the average age of the family is the same today. The present age of the baby is :

Question: Five years ago, the average age of A,B,C and D was `45` years .With E joing them now, the average of all the five is `49`.How old is E ?

Question: Five years ago, The average age of Q was `15` years. A average age of P,Q and R today is `20` years. How old will R be after `10` years ?

Question: The average age of boys in the class is twice the number of girls in the class.If the ratio of boys and girls in the class of `36` be `5 : 1`,what is the total of the ages (in years) of the boys in the class ?