The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?
Answer: A
Write the condition algebraically.
\[ A + B = (B + C) + 12 \]
The \( B \) cancels from both sides:
\[ A - C = 12 \]
So C is 12 years younger than A. B's age never matters - which is why it is not given.
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A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Answer: A
Let the son's present age be \(x \) years .
Then, \(\left ( 38-x \right )=x\)
\(\Rightarrow \) \(2x=38 \)
\(\Rightarrow x=19 \)
\( \therefore \) Son's age 5 years back (19-5) = 14 years
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One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Answer: C
Let the age of Sooraj and Vimal, 1 year ago, be \(6x\) and \(7x\) respectively
Given that, four years hence, this ratio would become 7:8
\(⇒ ( 6 x + 5 ) : ( 7 x + 5 ) = 7 : 8\)
\(⇒ 8 ( 6 x + 5 ) = 7 ( 7 x + 5 )\)
\(⇒ 48 x + 40 = 49 x + 35\)
\(⇒ x = 5 \)
Vimal's present age = \(7 x + 1 = 7 × 5 + 1 = 36 \) years
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At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
Answer: B
Let the present ages of Arun and Deepak be \(4x\) years and \(3x\) years respectively . Then ,
\(4x+6=26\)
\( \Rightarrow 4x=20\)
\(\therefore x=5\)
Now, Deepak's age = \(3x\) = 15
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The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
Answer: C
Let age of Sunil = \(x \) years and age of syam be = \(y\) years
\(x y = 240 ⋯ ( 1 )\)
\(2 x = y + 4\)
\(⇒ y = 2 x − 4\)
\(⇒ y = 2 ( x − 2 ) ⋯ ( 2 )\)
Substituting equation \((2)\) in equation \((1)\) we get ,
\(x × 2 ( x − 2 ) = 240\)
\(⇒ x ( x − 2 ) = \) \(\frac{240}{2}\)
\(⇒ x ( x − 2 ) = 120 ⋯ ( 3 )\)
We got a quadratic equation to solve.
Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way.
But it is more easy to substitute the values given in the choices in the quadratic equation (equation 3) and see which choice satisfy the equation.
Here, option A is 10. If we substitute that value in the quadratic equation,
\(x ( x − 2 ) = 10 × 8\) which is not equal to 120
Now try option B which is 12. If we substitute that value in the quadratic equation,
\(x
(
x
−
2
)
=
12
×
10
=
120
\) See, we got that \(x=12\)\
Hence Sunil's age = 12
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The average age of 80 boys in a class is 15. The average age of group of 15 boys in the class is 16 and the average of another 25 boys in the class is 14. What is the average age of the remaining boys in the class ?
Answer: D
otal ages of 80 boys = 15 x 80 = 1200 yrs.
Total age of 16 boys = 15 x 16 = 240 yrs
Total age of 25 boys = 14 x 25 = 350 yrs.
Average age of remaining boys = \(1200 - \frac{240+350}{80}-\left ( 25+15 \right )\)= \(\frac{610}{41}\)
= 15.25 yearss
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The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
Answer: C
Write the condition algebraically.
\[ A + B = (B + C) + 12 \]
The \( B \) cancels from both sides:
\[ A - C = 12 \]
So C is 12 years younger than A. B's age never matters - which is why it is not given.
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Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
Answer: C
Let Rahul's age be \(x \) years .
Then, Sachin's age = \((x-7)\) years
\(\therefore \) \(\frac{x - 7}{x}=\frac{7}{9}\)
\(\Rightarrow 9x - 63 = 7x\)
\(\Rightarrow 2x = 63\)
\(\Rightarrow x = 31.5\)
Hence, Sachin's age = \((x-7)\) = 24.5 years
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