General Mathematics

Question: If `x%` of a is the same as `y%` of b, then `z%` of b is
A
`(yz)/x% f a`

B
`(xy)/z% of a`

C
`(xz)/y % of a`

D
None of these

Note: `x% of a` `= y% of b ⇒ x/100 a` `= y/100 b ⇒ b` `= (x/100 xx 100/y) a` `= (x/y) a` `:. z% of b` `= (z% of x/y) a` `= ((xz)/(y xx 100)) a` `= ((xz)/y)% of a.`
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Question: In a city, `35%` of the population is composed of migrants,` 20%` of whom are from rural areas. Of the local population, `48%` is female while this figure for rural and urban migrants is `30%` and `40%` respectively. If the total population of the city is `728400,` what is its female population ?
A
`324138`

B
`349680`

C
`509940`

D
None

Note: Migrants`= 35% of 728400` `= 35/100 xx 728400` `= 254940`. Local population `= (728400 - 254940)` `= 473460` Rural population Urban population `= (254940 - 94692)` `= 160248` :. Female population `= 48% of 473460 + 30% of 94692 + 40% of 160248` `= (48/100 xx 473460 + 30/100 xx 94692 + 40/100 xx 160248)` `= 227260.8 + 28407.6 + 64099.2` `= 896660.
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Question: A's marks in Biology are `20` less than `25%` of the total marks obtained by him in Biology, Maths and Drawing. If his marks in Drawing be `50` what are his marks in Maths ?
A
`40`

B
`45`

C
`50`

D
Can't be determined

Note: Let B + M + D = x. Then, `B = (25% of x - 20)` `= (25/100 x - 20)` `= (x/4 - 20) & d = 50` `:. x/4 - 20 + M + 50` `= x or M = ((3x)/4 - 30)` So, marks in Maths cannot be determined
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Question: An increase of Rs. `60` in the monthly salary of Madam made it `50%` of the monthly salary of kamal. What is Madam' s present monthly salary ?
A
Rs. 180`

B
`Rs. 240`

C
`Rs. 300`

D
Data inadequate

Note: `M + 60` `= 50% of K.` Clearly, M cannot be determined
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Question: From a container having pure milk,` 20%` is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is :
A
`40% pure`

B
`50% pure`

C
`51.2% pure`

D
`58.8% pure`

Note: Let total quantity of original milk `= 1000 gm.` Milk after first operation `= 80% of 1000` `= 800 gm.` Milk after second operation `= 80% of 800` `= 640 gm.` Milk after third operation `= 80% of 640` `= 512 gm.` :. Strength of final mixture `= 51`2%`
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Question: A man bought a house for Rs.` 5` lakhs and rents it. He puts `12 1/2%` of each month's rent aside for repairs, pays Rs.`1660` as annual taxes and realises `10%` on his investment thereafter. The monthly rent of the house is :
A
`Rs. 5000`

B
`Rs. 4920`

C
`Rs. 2500`

D
`Rs. 2460`

Note: Suppose monthly rent = Rs. x Then, `12x - (25)/2% of 12x - 1660` `⇒ 10% of 500000` `⇒ 12x - (25)/200 xx 12x - 1660` `⇒ 500000` `⇒ (21x)/2` `= 51660 or x` `= (51660 xx 2/21)` `= 4920.`
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Question: In a public school, `1/5 th` of the girls and `1/4 th` of boys are under `12` years of age. If the total strength of the school is `1000` and number of girls is `2/5 th` of the total, what part of the total strength of the school is accounted for by those which are `12` years or more of age ?
A
`23%`

B
`45%`

C
`55%`

D
`77%`

Note: Girls` = (2/5 xx 1000)` `= 400,` Boys `= 600` Under `12` years `= (1/5 xx 400 + 1/4 xx 600)` `= 230` Above `12` years `= (1000 - 230)` `= 770.` Required percentage `= (770/1000 xx 100)%` `= 77%`.
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Question: A certain number of men can finish a piece of work in `100` days. If however, there were `10` men less, it would take `10` days more for the work to be finished. How many men were there originally ?
A
`75`

B
`82`

C
`100`

D
`110`

Note: Originally let there be `x` men. Less men, more days (Indirect) `:. (x - 10) : x :: 100 : 110` or `(x - 10)/x = (100)/(110)` or `11x - 110 = 10x` or `x = 110`. So, originally there were `110` men.
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Question: The salaries of A and B together amount to Rs.`2000.` A spends `95%` of his salary and B,` 85%` of his. If now, their saving are the same, what is A's salary ?
A
`Rs. 1500`

B
`Rs. 1250`

C
`Rs. 750`

D
`Rs. 1600`

Note: Let A's salary = x. Then, B's` = (2000 - x)` `5% of A` `= 15% of B, i. e. 5/100 x` `= 15/100 (2000 - x) or x` `= 1500.`
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Question: A certain number of men could do a piece of work in `60` days. If there were `8` more men, it could be finished in `10` days less. The number of men in the beginning were :
A
`30`

B
`35`

C
`40`

D
`45`

Note: Let `x` men can finish the work in `60` days. Then, `(x + 8)` men can finish it in `50` days. More men, less days (Indirect) `:. x + 8 : x = 60 : 50` or `(x + 8)/x = (60)/(50)` or `50 (x + 8) = 60x ` or `x = 40`. `:.` Number of men in the beginning `= 40`.
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Question: If `x%` of a is the same as `y%` of b, then `z%` of b is

Question: A's marks in Biology are `20` less than `25%` of the total marks obtained by him in Biology, Maths and Drawing. If his marks in Drawing be `50` what are his marks in Maths ?

Question: An increase of Rs. `60` in the monthly salary of Madam made it `50%` of the monthly salary of kamal. What is Madam' s present monthly salary ?

Question: From a container having pure milk,` 20%` is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is :

Question: A man bought a house for Rs.` 5` lakhs and rents it. He puts `12 1/2%` of each month's rent aside for repairs, pays Rs.`1660` as annual taxes and realises `10%` on his investment thereafter. The monthly rent of the house is :

Question: A certain number of men can finish a piece of work in `100` days. If however, there were `10` men less, it would take `10` days more for the work to be finished. How many men were there originally ?

Question: The salaries of A and B together amount to Rs.`2000.` A spends `95%` of his salary and B,` 85%` of his. If now, their saving are the same, what is A's salary ?

Question: A certain number of men could do a piece of work in `60` days. If there were `8` more men, it could be finished in `10` days less. The number of men in the beginning were :