General Mathematics

Question: A rope makes `70` rounds of the circumference of a cylinder whose radius of the base is `14` cm. How many times can it go round a cylinder with radius `20` cm ?
A
`40`

B
`49`

C
`100`

D
None of these

Note: More Radius, less rounds (Indirect) `20 : 14 :: 70 : x` or `20x = 14 xx 70` or `x = ((14 xx 70)/(20))` `= 49`. `:.` Required number of rounds `= 49`.
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Question: A debtor can pay `87` paise in the rupee, but if his creditors would take `20%` of his debts he could pay them and have Rs. `42` left. His debts and assets respectively are
A
`Rs. 600, Rs. 522`

B
`Rs. 500, Rs. 521`

C
`Rs. 400, Rs. 520`

D
`Rs. 1000, Rs. 525`

Note: Let the total debt = x. Asset with him `= 87/(100) x.` After paying `20%` of the debt, he is left with `80%` of the debt plus Rs.` 42.` `:. 80% of x + 42` `= 87/(100) x or 87/(100) x - 80/(100) x` `= 42 or x = 600.` :. Debt `= Rs. 600 &` Assets `= 87/100 xx 600` `= Rs. 522.`
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Question: `300` grams of sugar solution has `40%` sugar in it.How much sugar should be added to make it `50%` in the solution ?
A
`10 gms`

B
`40 gms`

C
`60 gms`

D
`80 gms`

Note: Sugar`= (40/100 xx 300) gms` `= 120 gms, water`= 180 gms` Let x gm sugar may be added. Then,(120 + x)/(300 + x) xx 100` `= 50 ⇒ 240 + 2x` `= 300 + x ⇒ x = 60.`
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Question: The quantity of water (in ml) needed to reduce `9` ml shaving lotion containing `50%` alcohol to a lotion containing `30%`alcohol, is :
A
`4`

B
`5`

C
`6`

D
`7`

Note: Alcohol in `9` ml `= (50/100 xx 9) ml` `= 4.5 ml`, water` = 4.5 ml.` Let the water to be added be x ml. Then,`(4.5)/(9 + x) xx 100` `= 30 ⇒ 450` `= 270 + 30x ⇒ x = 6 ml`
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Question: To a sugar solution of `3` litres containing `40%` sugar, one litre of water is added. The percentage of sugar in the new solution is :
A
`13 1/3%`

B
`15%`

C
`30%`

D
`33%`

Note: Sugar` = (40/100 xx 3) litres` `= 1.2 litres,` water`= 1.8 litres` New percentage`= (1.2/4 xx 100)%` `= 30%`
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Question: The price of an article is cut by `20%`. To restore it the former value, the new price must be increased by :
A
`20%`

B
`25%`

C
`16 2/3%`

D
`24%`

Note: Let original price`= 100`. New price`= 80` Increase on`80 = 20` Increase on`100 = (20/80 xx 100)%` `= 25%`.
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Question: The income of a broker remains unchanged though the rate of commission is increased from `4%` to `5%`. The percentage of slump is business is :
A
`1%`

B
``8%`

C
`20%`

D
`80%`

Note: Let the business value changes from x to y. `4% of x` `= 5% of y ⇒ 4/(100) x` `= 5/(100) y ⇒ y` `= 4/(5) x.` change in business `= (x - 4/5 x)` `= x/5` percentage slump `= (x/5 xx 1/x xx 100)%` `= 20%`
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Question: In an examination, there are `3` papers of Mathematics of `100` marks each. A boy secures `60%` in the first paper and `70%` in the second paper. In order to secure `705` in the aggregate the percentage of marks he should secure in third paper will be :
A
`90%`

B
`80%`

C
`75%`

D
`70%`

Note: `60 + 70 + x` `= 70/100 xx 300 or x` `= 80%`
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Question: If `3/5` of a cistern is filled in `1` minute, how much more time will be required to fill the rest of it ?
A
`30` sec

B
`40` sec

C
`36` sec

D
`24` sec

Note: Remaining part `= (1 - 3/5)` `= 2/5`. Less part, less time (Direct) `3/5 : 2/5 :: 60 : x`or `3/5 x = 2/5 xx 60` or `x = 40` sec. `:.`Rest of the cistern will be filled in `40` sec.
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Question: Ten pipes through which water flows at the same rate can fill a tank in `28` minutes. If three pipes go out of order, how long will the remaining pipes take to fill the tank ?
A
`40` min

B
`8` min `24` sec

C
`25` min `12` sec

D
`32` min `36` sec

Note: Less pipes, more time (Indirect) `:. 7 : 10 :: 28 : x` or `7x = 10 xx 28` or `x = (10 xx 28)/7` `= 40`. `:.`Remaining pipes will fill the tank in `40`min.
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Question: A rope makes `70` rounds of the circumference of a cylinder whose radius of the base is `14` cm. How many times can it go round a cylinder with radius `20` cm ?

Question: A debtor can pay `87` paise in the rupee, but if his creditors would take `20%` of his debts he could pay them and have Rs. `42` left. His debts and assets respectively are

Question: `300` grams of sugar solution has `40%` sugar in it.How much sugar should be added to make it `50%` in the solution ?

Question: The quantity of water (in ml) needed to reduce `9` ml shaving lotion containing `50%` alcohol to a lotion containing `30%`alcohol, is :

Question: To a sugar solution of `3` litres containing `40%` sugar, one litre of water is added. The percentage of sugar in the new solution is :

Question: The price of an article is cut by `20%`. To restore it the former value, the new price must be increased by :

Question: The income of a broker remains unchanged though the rate of commission is increased from `4%` to `5%`. The percentage of slump is business is :

Question: In an examination, there are `3` papers of Mathematics of `100` marks each. A boy secures `60%` in the first paper and `70%` in the second paper. In order to secure `705` in the aggregate the percentage of marks he should secure in third paper will be :

Question: If `3/5` of a cistern is filled in `1` minute, how much more time will be required to fill the rest of it ?

Question: Ten pipes through which water flows at the same rate can fill a tank in `28` minutes. If three pipes go out of order, how long will the remaining pipes take to fill the tank ?