Mathematics Mcqs

6 – [5/6 + {3 7/8 – 2 1/3 + 1 7/9}] = _____________?

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6 – [5/6 + {3 7/8 – 2 1/3 + 1 7/9}] = _____________?

A. 3 9/13
B. 1 9/11
C. 2 11/72
D. None of these
Explanation:
6 – [5/6 + {3 7/8 – 2 1/3} + 1 7/9] => 6 – [5/6 + {3 1/8 – 7/3} + 16/9]
=> 6 – [5/6 + {(279 – 168 + 128)/72}] => 6 – 5/6 + 239/72
=> 6 – (60 + 239)/72 => 6 – 46 – 11/72
=> 2 – 11/72 => 1 + 1 – 11/72 => 1 + 61/72 = 1 61/72

Positive integers indicated by x and y satisfy 3 1/x * y 2/5 = 13 3/4, the fractions being in their lowest terms, then x = ? and y = ____________?

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Positive integers indicated by x and y satisfy 3 1/x * y 2/5 = 13 3/4, the fractions being in their lowest terms, then x = ? and y = ____________?

A. x = 4, y = 8
B. x = 4, y = 4
C. x = 2, y = 4
D. x = 8, y = 4
Explanation:
3 1/x * y 2/5 = 13¾
=> (3x + 1) / x + (5y + 1) / 2 += 55 / 4
only choice (4) i.e x = 8 and y = 4 satisfies the given equation.
3 (1/8) * 4 (2/5) = (25 / 8 ) * (22 / 5) = 55/4 = 13¾

(830 + ? * 3 * 14 / 100) – (830 * 14 * 3 / 100) = 20.16

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(830 + ? * 3 * 14 / 100) – (830 * 14 * 3 / 100) = 20.16

A. 24
B. 36
C. 48
D. None of these
Explanation:
(830 + ? * 3 * 14 / 100) – (830 * 14 * 3 / 100) = 20.16
=> 830 + ? * 42 – 830 * 42 = 2016
=> ? * 42 = 2016 + 830 * 42 – 830
=> ? * 42 = 42 * 48 + 830 * 42 – 830
=> ? = 48 + 830 – (830 / 42)
=> ? = 48 + 830 – 19.76
=> ? = 858.24

A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is_______?

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A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is_______?

A. 3m
B. 5m
C. 8.75m
D. 10m

Explanation:
Area of the field = (38 x 32)m2
Let the width of the path be x metres
Area with out path = (38-2x)(32-2x)m2
= 1216+4×2 -140x
Area of the path = 1216 –(1216 +4×2 -140x)
= 140x -4×2 140x -4×2 = 600
=> 4×2-140x +600 =0
=> x2 -35x +150 =0
=> (x-30)(x-5)=0
=> X =5 m