Percentage, General Mathematics

Question: Arvind spends `75%` of his income. His income is increased by `20%` and he increased his expenditure by `10%`. His savings are increased by :
A
`10%`

B
`25%`

C
`37 1/2%`

D
`50%`

Note: Let income `= 100` Expenditure `= 75 &` Savings `= 25.` New income `= 120,` New expenditure `= (110/100 xx 75)` `= 165/2` New savings `= (120 - 165/2)` `= 75/2.` Increase in savings `= (75/2 - 25)` `= 25/2.` Increase percent `= (25/2 xx 1/25 xx 100)%` `= 50%`
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Question: There are `600` boys in a hostel. Each plays either hockey or football or both. If `75%` play hockey and `45%` play football, how many play both ?
A
`48`

B
`60`

C
`80`

D
`120`

Note: n(A)`= (75/100 xx 600)` `= 450, n (B)` `= (45/100 xx 600)` `= 270` and `n(AuuB) = 600.` `:.n(AnnB) = n(A) + n(B) - n(AuuB)` `= (450 + 270 - 600)` `= 120.`
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Question: In a certain office, `72%` of the workers prefer tea and `445` coffee. If each of them prefers tea or coffee and `40` like both, the total number of workers in the office is :
A
`200`

B
`240`

C
`250`

D
`320`

Note: Let total number be x. Then, `n(A) = 72/(100) x` `= (18x)/55, n(B)` `= (44)/(100) x` `= (11x)/25 & n(AnnB)` `= 40.` `n (AuuB) = n(A) + n(B) - n(AnnB)` `=> x = (18x)/25 + (11x)/25 - 40 => (29x)/25 - x` `= 40 or (4x)/25` `= 40` `:. x = ((25 xx 40)/4)` `= 250.`
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Question: In an examination, `80%` of the students passed in English, `85%` in Mathematics and `75%` in both English and Mathematics. If `40` students failed in both the subjects, the total number of students is :
A
`200`

B
`400`

C
`600`

D
`800`

Note: Let the total number of students be x. Number passed in one or both is given by : `n (AuuB) = n (A) + n (B) - n (AnnB)` `= 80% of x + 85% of x - 75% of x.` `= (80/(100) x + 85/(100) x - 75/(100) x)` `= 90/(100) x` `= (9x)/10.` Failed in both `= (x - (9x)/100)` `= x/10.` `:. x/10 = 40` `or x = 400`.
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Question: In an examination, `35%` candidates failed in one subject and `42%` failed in another subject while `15%` failed in both the subjects. If `2500` candidates appeared at the examination, how many passed in either subject but not in both ?
A
`325`

B
`1175`

C
`2125`

D
None of these

Note: Failed in 1st subject `= (35/100 xx 2500)` `= 875` Failed in 2nd subject `= (42/100 xx 2500)` `= 1050` Failed in both `= (15/100 xx 2500)` `= 375.` Failed in 1st subject only `= (875 - 375) = 500` Failed in 2nd subject only `= (1050 - 375)` `= 675.` Pleased in 2nd only + Passed in 1st only `= (675 + 500)` `= 1175.`
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Question: P is six times as large as q. The percent that q is less than p, is :
A
`83 1/3`

B
`16 2/3`

C
`90`

D
`60`

Note: p`= 6q,` so q is less than p by `5q.` Note that q has been compared with p. :. Required percentage `= ((5q)/p xx 100)%` `= ((5q)/(6q)) xx 100)%` `= 83 1/3%`
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Question: The boys and girls in a collage are in the ratio `3 : 2`. If `20%` of the boys and `25%` of the girls are adults, the percentage of students who are not adults is :
A
``58%`

B
`67.5%`

C
`78%`

D
`82.5%`

Note: Suppose boys `= 3x` and girls `= 2x` Not adults `= (80/100 xx 3x) + (75/100 xx 2x)` `= ((12x)/5 + (3x)/(2))` `= (39x)/10.` Required percentage `= ((39x)/10 xx 1/(5x) xx 100)%` `= 78%`
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Question: In an election between two candidates, a candidate who gets `40%` of total votes is defeated by `15000` votes. The number of votes polled by the winning candidate is :
A
`6000`

B
`10000`

C
`22500`

D
`45000`

Note: Let the votes polled by the winning candidate be x. Defeated candidate gets` (x - 15000)` votes. `40% of [x + (x - 15000)]` `= (x - 15000)` `2/5 (2x - 15000)` `= x - 15000` `or 4x - 30000` `= 5x - 75000` `or x = 45000.`
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Question: In an election between two candidate, one got `55%` of total valid votes `20%` of the votes were invalid. If the total number of votes was `750` the number of valid votes that the other candidates got was :
A
`2700`

B
`2900`

C
`3000`

D
3100`

Note: Valid votes in all `= 80% of 7500 = 6000` valid votes polled by another candidate `= 45% of 6000` `= (45/100 xx 6000)` `= 2700.`
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Question: At an election involving two candidate ,`68` votes were declared invalid .The winning candidate scores `5`%` and wins by `98` votes. The total number of votes polled is :
A
`2518`

B
`2450`

C
`2382`

D
None

Note: Let the valid votes be x Then, `52% of x - 48% of x` `= 98 => 4% of x = 98.` `:. 4/(100) x = 98` `or x = 98 xx 25` `= 2450.` :. Total votes polled `= (2450 + 68)` `= 2518.`
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Question: Arvind spends `75%` of his income. His income is increased by `20%` and he increased his expenditure by `10%`. His savings are increased by :

Question: There are `600` boys in a hostel. Each plays either hockey or football or both. If `75%` play hockey and `45%` play football, how many play both ?

Question: In a certain office, `72%` of the workers prefer tea and `445` coffee. If each of them prefers tea or coffee and `40` like both, the total number of workers in the office is :

Question: In an examination, `80%` of the students passed in English, `85%` in Mathematics and `75%` in both English and Mathematics. If `40` students failed in both the subjects, the total number of students is :

Question: In an examination, `35%` candidates failed in one subject and `42%` failed in another subject while `15%` failed in both the subjects. If `2500` candidates appeared at the examination, how many passed in either subject but not in both ?

Question: P is six times as large as q. The percent that q is less than p, is :

Question: The boys and girls in a collage are in the ratio `3 : 2`. If `20%` of the boys and `25%` of the girls are adults, the percentage of students who are not adults is :

Question: In an election between two candidates, a candidate who gets `40%` of total votes is defeated by `15000` votes. The number of votes polled by the winning candidate is :

Question: In an election between two candidate, one got `55%` of total valid votes `20%` of the votes were invalid. If the total number of votes was `750` the number of valid votes that the other candidates got was :

Question: At an election involving two candidate ,`68` votes were declared invalid .The winning candidate scores `5`%` and wins by `98` votes. The total number of votes polled is :