Fractions
 From a rope 30 m long, a person cuts off as many pieces as possible, each 3^{1}/_{4} m long. What fraction of the whole will be left ?

 1/40
 3/4
 8/13
 7/13

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Length of each piece = 3^{1}/_{4} = 13/4 m
Maximum pieces that can be cut = 30/(13/4) = 9
∴ Rope left = 30  13/4 x 9 = 120  117/4 = 3/4 m
∴ Required fraction = 3/4/30 = 1/4Correct Option: A
Length of each piece = 3^{1}/_{4} = 13/4 m
Maximum pieces that can be cut = 30/(13/4) = 9
∴ Rope left = 30  13/4 x 9 = 120  117/4 = 3/4 m
∴ Required fraction = 3/4/30 = 1/4
 If 0.3+ 0.6 + 0.7 + 0.8 = x, then x is equal to ?

 2^{3}/_{10}
 2^{2}/_{3}
 2.35
 5^{3}/_{10}

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0.3+ 0.6 + 0.7 + 0.8 = x,
⇒ x = 3/9 + 6/9 + 7/9 + 8/9 = 24/9 = 8/3Correct Option: B
0.3+ 0.6 + 0.7 + 0.8 = x,
⇒ x = 3/9 + 6/9 + 7/9 + 8/9 = 24/9 = 8/3 = 2^{2}/_{3}
 A boy on being asked 13/14 of a certain fraction had made the mistake of dividing the fraction by 14/13 and so got an answer that exceeded the correct answer by 3/65. The correct fraction is ?

 14/45
 12/65
 13/45
 2/7

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Let the fraction be N.
Then, N / (13/14)  (13/14) x N = 3/65Correct Option: C
Let the fraction be N.
Then, N / (13/14)  (13/14) x N = 3/65
⇒ 14N/13  13N/14 = 3/65
⇒ (196N  169N)/182 = 3/65
⇒ 27N/182 = 3/65
∴ N = (3 x 182) / (27 x 65) = 14/45
So, correct answer will be (13/14) x (14/45) = 13/45
 A man left (1/7)th of his property to his daughter and the remaining to his sons to be equally divided among them. If the share of the each son be double than that of the daughter. Then, find the number of sons ?

 2
 3
 6
 4

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Let the total property = N
Then, property of his daughter = P/7
∴ Remaining property = P  P/7 = 6P/7
Now, this property is divided among his sons, so that each son gets twice the property of his daughter.
Let number of sons be K.
Then, 6N/7 x K = 2N/7Correct Option: B
Let the total property = N
Then, property of his daughter = P/7
∴ Remaining property = P  P/7 = 6P/7
Now, this property is divided among his sons, so that each son gets twice the property of his daughter.
Let number of sons be K.
Then, 6N/7 x K = 2N/7
⇒ K = 3
 A vessel, full of water, weighs 16.5 kg. When the vessel is (1/4)th full, it weight 5.25 kg. Then, weight of the empty vessel (in kg) is ?

 1.125
 4.5
 1.5
 3

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Let the weight of vessel = x kg
Then, 1/4 of volume of water = (5.25  x)kg
Full volume of water = (16.5  x)
∴ 4(5.25  x)= (16.5  x)
Correct Option: C
Let the weight of vesel = x kg
Then, 1/4 of volume of water = (5.25  x)kg
Full volume of water = (16.5  x)
∴ 4(5.25  x) = (16.5  x)
⇒ 21  4x = 16.5  x
⇒ 21  16.5 = 3x
∴ x = 4.5/3 = 1.5 kg