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Question Detail
Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
- 10:3
- 5:9
- 11:9
- 13:9
Answer: Option C
Explanation:
\begin{aligned}
=> \frac{(x+y)}{(x-y)} = \frac{40}{4}
\end{aligned}
\begin{aligned}
=> (x+y)= 10(x-y)
\end{aligned}
\begin{aligned}
=> 9x = 11y => \frac{x}{y} = \frac{11}{9}
\end{aligned}
1. 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 is
- 15
- 20
- 25
- 35
Answer: Option 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}
2. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is
- 11
- 22
- 44
- 33
Answer: Option C
Explanation:
Let sons age = x. Then, fathers age = 2x.
12(x—2O) = (2x - 20) so x = 22
Fathers present age = 44 years
3. Find the number which when multiplied by 15 is increased by 196
- 10
- 12
- 14
- 16
Answer: Option C
Explanation:
Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.
4. 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
5. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is
- 20
- 23
- 27
- 150
Answer: Option 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}
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