The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Answer: B
Let their present ages be \(4x, 7x \) and \(9x\) years respectively
Then, \((4x - 8) + (7x - 8) + (9x - 8) = 56\)
\(\Rightarrow 20x = 80\)
\(\Rightarrow x=4\)
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Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Answer: C
Mother's age when Ayesha's brother was born = 36 years
Father's age when Ayesha's brother was born = \((38 + 4)\) years = 42 years
\(\therefore \) Required difference = \((42 - 36)\)years = 6 years
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Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
Answer: D
Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question : R - Q = ? .
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.
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The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Answer: B
Let the ages of father and son 10 years ago be \(3x\) and \(x\) years respectively
Then, \( (3x + 10) + 10 = 2[(x + 10) + 10]\)
\( \Rightarrow3x + 20 = 2x + 40\)
\(\Rightarrow x = 20.\)
\(\therefore\) Required ratio = \( (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.\)
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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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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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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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Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?
Answer: B
Let John's present age be \(x\)
\(\therefore \) \(x-5=\) \(\frac{1}{2}\left ( x+8 \right )\)
\(\Rightarrow \) \(x-5=\) \(\frac{1}{2}x +4\)
\(\Rightarrow \) \(\frac{1}{2}x=9\)
\(\Rightarrow \) \(x=18\)
Hence, John's is 18 years old.
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The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?
Answer: A
Let the present age of A and B be 5 \(x\) and 6 \(x\) respectively.
Therefore, According to problem,
5 \(x\) + 6 \(x\) = 44
\(\Rightarrow \) \(11x=44\)
\(\Rightarrow \) \(x =4\)
Present ages of A and B are 20 and 24 respectively.
After 8 years,
Ages of A and B are (20+8) and (24+8)
A = 28 years and B=32 years
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A mother said her daughter , " I was as old as you are at present at the time of your birth. " If the mother age is 38 now, the daughter age 5 years back was ?
Answer: A
Let the son's present age be \(x\) years .
Then, \( (38 - x) = x \)
\(=> x= 19\)
Son's age 5 years back = (19-5) = 14 yeara
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