Simplification, General Mathematics

Question: A number of friends decided to go on a picnic and planed to spend Rs `96` on eatables. Four of them ,did not turn up.As a consequence, the remaining ones had to contributed Rs `4` each extra.The number of these who attended the picic was
A
`24`

B
`16`

C
`12`

D
`8`

Note: Suppose total number = x.Then, `96/(x - 4) - 96/x = 4` `or 1/(x - 4) - 1/x = 4/96` `or x- (x - 4)/x(x - 4) = 1/24` `or x^2 - 4x - 96 = 0` `or (x - 12)(x + 8) = 0` `or x = 12`. :. Number of students attending the picnic `= (12 - 4) = 8`
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Question: A man distributed Rs `100` equally among his friends. If there had been `5` more friends, each would have received one upee less. How many friends had he /
A
`20`

B
`25`

C
`30`

D
`35`

Note: Suppose he had x friends. Then, `100/x - 100/(x + 5) = 1` `or 1/x - 1/(x + 5) = 1/100` `(x + 5 - x)/(x(x + 5)) = 1/100` `or x^2 + 5x - 500 = 0` `or (x + 25) (x - 20) = 0` `:. x = 20`.
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Question: In a group of cows and hens, the number of legs are `14` more than twice the number of heads. The number of cows is
A
`5`

B
`7`

C
`10`

D
`12`

Note: Let the number of cows be x and the number of hens be y.Then, `4x + 2y = 2(x +y) + 14` `or 2x + (2x + 2y)` `= (2x + 2y) + 14` `or 2x = 14` `or x = 7`.
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Question: An enterprising businessman earns an income of Rs `1` on the first day of his business.On every subsequent day ,he earns an income which is just double of that made on the previous day.On `10 th` day of business, he earns an income of :
A
`Rs 2^9`

B
`Rs 2^10`

C
Rs10^2`

D
`Rs`10`

Note: 2nd day he earns `= 2 = 2^(2-1)` 3rd day he earns `= 2^(3-1)` On `10 th`day he earns `2^(10- 1) = 2^9` rupees.
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Question: A number of friends decided to go on a picnic and planed to spend Rs `96` on eatables. Four of them ,did not turn up.As a consequence, the remaining ones had to contributed Rs `4` each extra.The number of these who attended the picic was

Question: A man distributed Rs `100` equally among his friends. If there had been `5` more friends, each would have received one upee less. How many friends had he /

Question: In a group of cows and hens, the number of legs are `14` more than twice the number of heads. The number of cows is

Question: An enterprising businessman earns an income of Rs `1` on the first day of his business.On every subsequent day ,he earns an income which is just double of that made on the previous day.On `10 th` day of business, he earns an income of :