Chain Rule, 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: 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: If `21` cows eat that much as `15` buffaloes , how many cows will eat that much as `105` buffaloes ?
A
`75`

B
`147`

C
`63`

D
None of these

Note: `15` buffaloes `-= 21` cows `105` buffaloes `-= ((21)/(15) xx 105)` cows `= 147` cows.
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Question: `95` men had provisions for `200` days. After `5` days, `30` men died due to an epidemic. The remaining food will last for how many days ?
A
`136 (16)/(19)` days

B
`180` days

C
`285` days

D
None of these

Note: The remaining food is sufficient for `95` men for `195` days. But, now remaining men `= (95 - 30) = 65`. Less men, More days (Indirect) `:. 65 : 95 :: 195 : x` or `65x = 95 xx 195` or `x = (95 xx 195)/(65)` `= 285`. Hence, the remaining food will last for `285` days.
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Question: A garrison of `500` men had provisions for `27` days. After `3` days, a reinforcement of `300` men arrived. The remaining food will now last for how many days ?
A
`15`

B
`16`

C
`17 1/2`

D
`18`

Note: The remaining food is sufficient for `500` men for `24` days. But, now the number of men `= (500 + 300) = 800`. More men, less days (Indirect) `800 : 500 :: 24 : x` or `800x = 500 xx 24` or `x = (500 xx 24)/800` `x = 15`. `:.` The food will now last for `15` days.
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Question: A garrison had provisions for a certain number of days. After `10` days `1/5`th of the men desert and it is found that the provisions will now last just as long as before. How long was that ?
A
`15` days

B
`25` days

C
`35` days

D
`50` days

Note: Initially, let there be `x` men having food for `y` days. After `10` days, `x` men had food for `(y - 10)` days. i.e. `(x - x/5)` or `(4x)/5` men had food for `y` days. `:. x (y - 10) = ((4x)/5)y` or `xy - 50x = 0` or `x (y - 50) = 0`. So, `y = 50 [ :. x != 0]`
1. Report

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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: 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 ?

Question: If `21` cows eat that much as `15` buffaloes , how many cows will eat that much as `105` buffaloes ?

Question: `95` men had provisions for `200` days. After `5` days, `30` men died due to an epidemic. The remaining food will last for how many days ?

Question: A garrison of `500` men had provisions for `27` days. After `3` days, a reinforcement of `300` men arrived. The remaining food will now last for how many days ?

Question: A garrison had provisions for a certain number of days. After `10` days `1/5`th of the men desert and it is found that the provisions will now last just as long as before. How long was that ?