1) Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the numb
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Ans. A
Explanation :
Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5
2) Sum of a rational number and its reciprocal is 13/6. Find the numb
- 1) 2
- 2) 3/2
- 3) 4/2
- 4) 5/2
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Ans. B
Explanation :
\begin{aligned} => x + \frac{1}{x} = \frac{13}{6} \end{aligned}
\begin{aligned} => \frac{x^2+1}{x} = \frac{13}{6} \end{aligned}
\begin{aligned} => 6x^2-13x+6 = 0 \end{aligned}
\begin{aligned} => 6x^2-9x-4x+6 = 0 \end{aligned}
\begin{aligned} => (3x-2)(2x-3) \end{aligned}
\begin{aligned} => x = 2/3 or 3/2 \end{aligned}
3) find the number, difference between number and its 3/5 is 5
- 1) 120
- 2) 123
- 3) 124
- 4) 125
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Ans. D
Explanation :
Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125
4) The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum
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Ans. B
Explanation :
Let the numbers be a, b and c.
Then,
\begin{aligned}
a^2 + b^2 + c^2 = 138
\end{aligned}
and (ab + bc + ca) = 131
\begin{aligned}
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
\end{aligned}
= 138 + 2 x 131 = 400
\begin{aligned}
=> (a + b + c) = \sqrt{400} = 20.
\end{aligned}
5) If one third of one fourth of number is 15, then three tenth of number
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Ans. C
Explanation :
Let the number is x,
\begin{aligned}
\frac{1}{3} of\frac{1}{4} * x = 15
\end{aligned}
\begin{aligned}
=> x = 15\times 12 = 180
\end{aligned}
\begin{aligned}
=> so \frac{3}{10} \times x = \frac{3}{10} \times 180 = 54
\end{aligned}
6) A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that numb
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Ans. A
Explanation :
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
7) Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the numb
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Ans. D
Explanation :
If the number is x,
Then, x + 17 = 60/x
x2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3, -20, so x = 3 (as 3 is positive)
8) The product of two numbers is 120 and the sum of their squares is 289. The sum of the number
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Ans. B
Explanation :
We know
\begin{aligned}
(x + y)^2 = x^2 + y^2 + 2xy
\end{aligned}
\begin{aligned}
=> (x + y)^2 = 289 + 2(120)
\end{aligned}
\begin{aligned}
=> (x + y) = \sqrt{529} = 23
\end{aligned}
9) Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer
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Ans. C
Explanation :
Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15
10) Find the number which when multiplied by 15 is increased by
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Ans. C
Explanation :
Let the number be x.
Then, 15x = x + 196
=â€º 14 x= 196
=â€º x = 14.