Fractions
- Sum of three fractions is 211/24. If the greatest fraction is divided by the smallest fraction, the result is 7/6, which is greater than the middle fraction by 1/3. find all the three fractions ?
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Let the fraction be x, y and z respectively in decreasing order.
Then, according to the question,
x/z = 7/6
⇒ x = 7z/6
And y = 7/6 - 1/3 = 7-2/6 = 5/6
Now, x + y + z = 211/24Correct Option: B
Let the fraction be x, y and z respectively in decreasing order.
Then, according to the question,
x/z = 7/6
⇒ x = 7z/6
And y = 7/6 - 1/3 = 7-2/6 = 5/6
Now, x + y + z = 211/24
⇒ 7z/6 + 5/6 + z = 59/24
⇒ (13z + 5)/ 6 = 59/24
⇒ 13z = 59/4 - 5 =39/4
⇒ z = 3/4
∴ x =7z/6 = 7/8
Hence, the fraction are 7/8, 5/6, 3/4.
- 1/8th part of a pencil is black, half of the remaining is white. If the remaining part is blue and length of this blue part is 31/2cm, then find the length of the pencil ?
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Let the total length of pencil = L cm
Then, black part = L/8
∴ Remaining part = L - L/8 = 7L/ 8
and White part = (7L/8)/2 = 7L/8
∴ Remaining part = L - (L/8 + 7L/16) = 7L/16
∴ length of blue part = 7L/16Correct Option: C
Let the total length of pencil = L cm
Then, black part = L/8
∴ Remaining part = L - L/8 = 7L/ 8
and White part = (7L/8)/2 = 7L/8
∴ Remaining part = L - (L/8 + 7L/16) = 7L/16
∴ length of blue part = 7L/16
According to the question,
7L/16 = 31/2
⇒ 7L/16 = 7/2
∴ L =8
- 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 ?
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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
- 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 ?
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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 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 ?
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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
