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Question Detail
Sum of a rational number and its reciprocal is 13/6. Find the number
- 2
- 3/2
- 4/2
- 5/2
Answer: Option 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}
1. A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
- 8
- 10
- 12
- 14
Answer: Option A
Explanation:
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
2. If one third of one fourth of number is 15, then three tenth of number is
- 34
- 44
- 54
- 64
Answer: Option 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}
3. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
- 12
- 13
- 15
- 17
Answer: Option 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
4. Two numbers differ by 5. If their product is 336, then sum of two number is
- 33
- 34
- 36
- 37
Answer: Option D
Explanation:
Friends you remember,
\begin{aligned}
=> (x+y)^2 = (x-y)^2 + 4xy
\end{aligned}
\begin{aligned}
=> (x+y)^2 = (5)^2 + 4(336)
\end{aligned}
\begin{aligned}
=> (x+y) = \sqrt{1369} = 37
\end{aligned}
5. find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.
- 214
- 216
- 114
- 116
Answer: Option B
Explanation:
Let the number is x,
\begin{aligned}
=> \frac{2}{3}x-50 = \frac{1}{4}x + 40
\end{aligned}
\begin{aligned}
<=> \frac{2}{3}x-\frac{1}{4}x = 90
\end{aligned}
\begin{aligned}
<=> \frac{5x}{12} = 90
\end{aligned}
\begin{aligned}
<=> x = 216
\end{aligned}
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