Chain Rule, General Mathematics

Question: The price of `357` mangoes is `Rs. 1517.25`. What will be the approximate price of `49` dozens of such mangoes ?
A
`Rs. 3000`

B
`Rs. 3500`

C
`Rs. 4000`

D
`Rs. 2500`

Note: More mangoes, more cost (Direct) `357 : 49 xx 12 :: 1517.25 : x` or `375 xx x = 49 xx 12 xx 1517.25`. `:. x = ((49 xx 12 xx 1517.25)/(357))` `= 2499`. `:.` Approximate cost `= Rs. 2500`.
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Question: The price of `438` oranges is `Rs. 1384.08`. What will be the approximate price of `8` dozens of oranges ?
A
`Rs. 300`

B
`Rs. 400`

C
`Rs. 500`

D
`Rs. 250`

Note: Less oranges, less cost (Direct) `438 : 96 :: 1384.08 : x` or `x = (96 xx 1384.08)/(438)` `= 303.36`. `:.` Approximate cost `= Rs. 300`.
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Question: If `11.25`m of a uniform iron rod weighs `42.75`kg , what will be the weight of `6` m of the same rod ?
A
`22.8`kg

B
`25.6`kg

C
`28`kg

D
`26.5`kg

Note: Less length, less weight (Direct) `:. 11.25 : 6 :: 42.75 : x` or `x = ((6 xx 42.75)/(11.25))` `= 22.8`. `:.` Weight of `6` m long rod `= 22.8` kg.
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Question: On a scale of a map, `0.6`cm represents `6.6`kg. If the distance between two points on the map is `80.5`cm, the actual distance between these points is :
A
`9`kg

B
`72.5`kg

C
`190.75`kg

D
`885.5`kg

Note: More distance on the map, more actual distance (Direct) `0.6 : 80.5 :: 6.6 : x` or `0.6x = 80.5 xx 6.6` or `x = ((80.5 xx 6.6)/(0.6))` `= 885.5` kg. Hence, actual distance `= 885.5` km.
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Question: If `20` men working together can finish a job finish a job in `20` days, then the number of days taken by `25` men of the same capacity to finish the job is :
A
`25`

B
`20`

C
`16`

D
`12`

Note: More men, less days (Indirect) `25 : 20 :: 20 : x` or `25x = 20 xx 20` or `x = ((20 xx 20)/(25))` `= 16`. `:.`Required number of days `= 16`
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Question: If `10` men can reap a field in `8` days, then `8` men will reap the same field in :
A
`5` days

B
`4` days

C
`10` days

D
`20` days

Note: Less men, more days (Indirect) `8 : 10 :: 8 : x` or `8x = 10 xx 8` or `x = ((10 xx 8)/8)` `= 10`. `:.` Required number of days `=10`.
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Question: `14` pumps of equal capacity can fill a tank in 6 days. If the tank has to be filled in `4` days, the number of extra pumps needed is :
A
`7`

B
`14`

C
`21`

D
`28`

Note: Less days, more pumps (Indirect) `4 : 6 :: 14 : x` or `4x = 6 xx 14` or `x = ((6 xx 14)/4)` `= 21`. `:.` Extra pumps needed `=(21 - 14)` `= 7`.
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Question: If `16` men working `7` hours a day can plough a field in `48` days, in how many days will `14` men working `12` hours a day plough the same field ?
A
`46`

B
`35`

C
`32`

D
`30`

Note: Less men, more days (Indirect) More hrs/day, less days (Indirect) men `{:(14 : 16 text(Hrs/Day,)),(12 : 7 )} :: 48 : x` `:. 14 xx 12 xx x = 16 xx 7 xx 48` or `x = ((16 xx 7 xx 48)/(14 xx 12))` `= 32`. `:.` Required number of days `= 32`.
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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: 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: The price of `357` mangoes is `Rs. 1517.25`. What will be the approximate price of `49` dozens of such mangoes ?

Question: The price of `438` oranges is `Rs. 1384.08`. What will be the approximate price of `8` dozens of oranges ?

Question: If `11.25`m of a uniform iron rod weighs `42.75`kg , what will be the weight of `6` m of the same rod ?

Question: On a scale of a map, `0.6`cm represents `6.6`kg. If the distance between two points on the map is `80.5`cm, the actual distance between these points is :

Question: If `20` men working together can finish a job finish a job in `20` days, then the number of days taken by `25` men of the same capacity to finish the job is :

Question: If `10` men can reap a field in `8` days, then `8` men will reap the same field in :

Question: `14` pumps of equal capacity can fill a tank in 6 days. If the tank has to be filled in `4` days, the number of extra pumps needed is :

Question: If `16` men working `7` hours a day can plough a field in `48` days, in how many days will `14` men working `12` hours a day plough the same field ?

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: 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 :