General Mathematics

Question: If the the length and breadth of a rectangular plot are increased by `50%` and `20%`respectively, then the new area is how many times the original area
A
`5/9`

B
`10`

C
`9/5`

D
None of these

Note: Not available
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Question: A box contains `Rs. 56` in the form of coins of one rupee, `50-` paise and `25-` paise. The number of `50-` paise coins is double the number of `25` paise coins and four times the number of one rupee coins. How many `50` paise coins are there in the box ?
A
`64`

B
`32`

C
`16`

D
Data inadequate

Note: Let rupee coins `= x, 50-`paise coins `= 4x` and `25-` paise coins `= 2x`. `:.` Ratio of these coins `x : 4x : 2x = 1 : 4 : 2`. Ratio of their values `= 1/1 : 4/2 : 2/4 = 4 : 8 : 2 = 2 : 4 : 1`. `:.` Value of `50-` paise coins `= Rs. (56 xx 4/7)` `= Rs. 32`. Number of `50-` paise coins `= 64`.
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Question: In a cash bag there are currency notes in denominations of `Rs. 20` Rs. 10` and `Rs. 5` in the ratio `3 : 4 : 5`. If the total amount in the bag is `Rs. 1000`, the number of five-rupee notes is :
A
`40`

B
`36`

C
`30`

D
`25`

Note: Ratio of the number of `Rs. 20, Rs. 10, Rs. 5` notes `= 3 : 4 : 5`. Ratio of their values `= 60 : 40 : 25 = 12 : 8 : 5`. Value of five-rupee notes `=Rs. (1000 xx 5/(25))` `= Rs. 200`. Number of five-rupee notes `= ((200 )/5) = 40`.
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Question: A purse contains one-rupee, `50-` paise, `25-` paise and `20-` paise coins in the ratio of `1 : 2 : 4 : 5`. If the total value of coins is `Rs. 400`, then the number of `20-` paise coins exceeding those of `25-` paise coins is :
A
`100`

B
`200`

C
`400`

D
`500`

Note: Ratio of values `= 1/1 : 2/2 : 4/4 : 5/5 = 1 : 1 : 1 : 1`. Value of `20` paise coins `= Rs. (400 xx 1/4) = Rs. 100`. Number of `20` paise coins `= (100 xx 5) = 500`. Value of `25` paise coins `= Rs. (400 xx 1/4) = Rs. 100`. Number of `25` paise coins `= (100 xx 4) = 400`. Difference in number of `20-` paise & `25-`paise coins `= 100`.
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Question: In a school, `10%` of the boys are same in number as `1/4`th of the girls and `10%` of the girls are same in number as `1/(25)`th of the boys. What is the ratio of boys to girls in that school ?
A
`3 : 2`

B
`5 : 2`

C
`2 : 1`

D
`4 : 3`

Note: `(10)/(100) B = 1/4 G` and `(10)/(100) G = 1/(25) B` `2B - 5G = 0 ` and `5G - 2B = 0`. `:. 2B = 5G` or `B/G = 5/2`.
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Question: The incomes of `A, B, C` are in the ratio of `7 : 9 : 12` and their spendings ate in the ratio of `8 : 9 : 15`. If `A` saves `1/4`th of his income, then the savings of `A, B, C` are in the ratio of :
A
`56 : 99 : 69`

B
`99 : 56 : 69`

C
`69 : 56 : 99`

D
`99 : 69 : 56`

Note: Let their incomes be `7x, 9x` and `12x` and their spendings be `8y, 9y` and `15y`. Theb, their saving are `(7x - 8y), (9x - 9y) & (12x - 15y)`. Now, `7x - 8y = (7x)/4` or `21x = 32y` or `x/y = (32)/(21)`. `:. (7x - 8y)/(9x - 9y) =(7 (x/y) - 8)/(9 (x/y) - 9)` `= (7 xx ((32)/(21)) - 8)/(9 xx ((32)/(21)) - 9)` `= 8/3 xx 7/(33)` `= (56)/(99)`. `(9x - 9y)/(12x - 15y) = (9 (x/y) - 9)/(12 (x/y) - 15)` `= (9 xx (32)/(21) - 9)/(12 xx (32)/(21) - 15)` `= (33)/(23)` `= (99)/(69)`. `:.` Ratio of savings `= 56 : 99 : 69`.
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Question: If `76` is divided into four parts proportional to `7, 5, 3, 4,` the smallest part is :
A
`12`

B
`15`

C
`16`

D
`19`

Note: Given Ratio is `7 : 5 : 3 : 4`. `:.` Smallest part `= (76 xx 3/(19))` `= 12`.
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Question: Ramlal divided two sums of money among his four sons Anil, Rahul, Deepak and Sanjeev. The first sum is divided in the ratio `4 : 3 : 2 : 1` and second in the ratio `5 : 6 : 7 : 8`. If the second sum is twice the first, the largest total is received by :
A
Anil

B
Rahul

C
Deepak

D
Sanjeev

Note: Let their parts in first sum be `4x, 3x, 2x` and `x`and let their parts in second sum be `5y, 6y, 7y` and `8y`. `:. 2(4x + 3x + 2x + x) = (5y + 6y + 7y + 8y)` or `20x = 26y` or `x = (13)/(10)y`. `:. A = 4x + 5y` `= 4 xx (13)/(10)y + 5y` `= (102y)/(10)` `= 10.2y,` `R = 3x + 6y` `= 3 xx (13)/(10)y + 6y` `= (99y)/(10)` `= 9.9y,` `D = 2x + 7y` `= 2 xx (13)/(10)y + 7y` `= (96y)/(10)` `= 9.6y,` `S = x + 8y` `= (13)/(10)y + 8y` `=(93y)/(10)` `= 9.3y`. So, Anil received the largest total.
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Question: A man rows `750` seconds against the stream and returns in `7 1/2` minutes. His rowing speed in still water is :
A
`3 km∕hr`

B
`4 km∕hr`

C
`5 km∕hr`

D
`6 km∕hr`

Note: Rate upstream `= (750/675) m∕sec` `= 10/9 m∕sec` Rate downstream `= (750/450) m∕sec` `= 5/3 m∕sec.` Rate in still water `= 1/2 (10/9 + 5/3) m/sec` `= 25/18 m∕sec.` `= (25/18 xx 18/5) kmph` `= 5 kmph.`
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Question: If a boat goes `7` km upstream in `42` minutes and the speed of the stream is `3` kmph, then the speed of the boat in still water is :
A
`4.2 km/hr`

B
`9 km/hr`

C
`13 km/hr`

D
`21 km/hr`

Note: Rate upstream `= (7/42 xx 60) kmph` `= 10 kmph` Speed of stream `= 3 kmph` Let speed in still water be x km/hr Then, speed upstream `= (x - 3) km/hr` `:. x - 3 = 10` ` or x = 13 kmph`
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Question: If the the length and breadth of a rectangular plot are increased by `50%` and `20%`respectively, then the new area is how many times the original area

Question: A box contains `Rs. 56` in the form of coins of one rupee, `50-` paise and `25-` paise. The number of `50-` paise coins is double the number of `25` paise coins and four times the number of one rupee coins. How many `50` paise coins are there in the box ?

Question: In a cash bag there are currency notes in denominations of `Rs. 20` Rs. 10` and `Rs. 5` in the ratio `3 : 4 : 5`. If the total amount in the bag is `Rs. 1000`, the number of five-rupee notes is :

Question: A purse contains one-rupee, `50-` paise, `25-` paise and `20-` paise coins in the ratio of `1 : 2 : 4 : 5`. If the total value of coins is `Rs. 400`, then the number of `20-` paise coins exceeding those of `25-` paise coins is :

Question: In a school, `10%` of the boys are same in number as `1/4`th of the girls and `10%` of the girls are same in number as `1/(25)`th of the boys. What is the ratio of boys to girls in that school ?

Question: The incomes of `A, B, C` are in the ratio of `7 : 9 : 12` and their spendings ate in the ratio of `8 : 9 : 15`. If `A` saves `1/4`th of his income, then the savings of `A, B, C` are in the ratio of :

Question: If `76` is divided into four parts proportional to `7, 5, 3, 4,` the smallest part is :

Question: Ramlal divided two sums of money among his four sons Anil, Rahul, Deepak and Sanjeev. The first sum is divided in the ratio `4 : 3 : 2 : 1` and second in the ratio `5 : 6 : 7 : 8`. If the second sum is twice the first, the largest total is received by :

Question: A man rows `750` seconds against the stream and returns in `7 1/2` minutes. His rowing speed in still water is :

Question: If a boat goes `7` km upstream in `42` minutes and the speed of the stream is `3` kmph, then the speed of the boat in still water is :