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Question 1 of 5
1. Question
While travelling with my friend in his car, I asked him how old the car was, on which he replied, ‘I am twice as old as my car was when I was as old as my car is now’. If the combined age of my friend and his car is seventy years, then what is my friend’s age?
Correct
Answer: Option (b)
Explanation:
Let the car be x years old and person be y years old.
Let us focus on the statement: I am twice as old as my car was when I was as old as my car is now.
So, the friend is talking about the age of the car when he was x years old, i.e. (y – x) years ago.
Age of the car (y – x) years ago = x – (y – x) = 2x – y
According to the question,
y = 2 (2x – y)
or 3y = 4x … (i)
Also, x + y = 70 … (ii)
Putting value of x from equation (ii) in equation (i), we get:
3y = 4 (70 – y)
or 3y = 280 – 4y
or 7y = 280
or y = 40
Hence, present age of my friend is 40 years.
Incorrect
Answer: Option (b)
Explanation:
Let the car be x years old and person be y years old.
Let us focus on the statement: I am twice as old as my car was when I was as old as my car is now.
So, the friend is talking about the age of the car when he was x years old, i.e. (y – x) years ago.
Age of the car (y – x) years ago = x – (y – x) = 2x – y
According to the question,
y = 2 (2x – y)
or 3y = 4x … (i)
Also, x + y = 70 … (ii)
Putting value of x from equation (ii) in equation (i), we get:
3y = 4 (70 – y)
or 3y = 280 – 4y
or 7y = 280
or y = 40
Hence, present age of my friend is 40 years.
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Question 2 of 5
2. Question
An old lady spent one twelfth of her life as a child and one seventh was spent as a teenager. One sixth of her life was spent between the time she became an adult and the time she married. Three years after marriage her daughter was born and the daughter died six years before she died. She lived to be twice as old as her daughter did. How long did the lady’s daughter live?
Correct
Answer: Option (b)
Explanation:
Let the age of the lady at the time of her death be X.
Age spent as child = X/12
Age spent as a teenager = X/7
Age spent between adulthood and marriage = X/6
Age of daughter = X – (X/12 + X/7 + X/6 + 3 + 6) = X – 33X/84 – 9 = 51X/84 – 9
Now, 2(51X/84 – 9) = X
Or 18X/84 = 18
Or X = 84.
Age of daughter = X/2 = 84/2 = 42 years
Incorrect
Answer: Option (b)
Explanation:
Let the age of the lady at the time of her death be X.
Age spent as child = X/12
Age spent as a teenager = X/7
Age spent between adulthood and marriage = X/6
Age of daughter = X – (X/12 + X/7 + X/6 + 3 + 6) = X – 33X/84 – 9 = 51X/84 – 9
Now, 2(51X/84 – 9) = X
Or 18X/84 = 18
Or X = 84.
Age of daughter = X/2 = 84/2 = 42 years
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Question 3 of 5
3. Question
In year 2010 Gautam is 36 years old, and his son is 8 years old. Then which of the following is correct?
Correct
Answer: Option (c)
Explanation:
Present age of Gautam = 36 years
His son‘s age = 8 years
We will solve this by options.
(a)
In year 2014, i.e. after 4 years from 2010:
Gautam‘s son‘s age = 8 + 4 = 12 years and its thrice value = 36 years
∴ After 4 years, age of Gautam = 36 + 4 = 40 years
Hence, in year 2014, Gautam‘s age will not be thrice of his son‘s age.
Hence, option (a) is incorrect.
(b)
In year 2020, i.e. after 10 years from 2010:
Gautam‘s son‘s age = 8 + 10 = 18 years and its thrice value = 54 years
∴ After 10 years, age of Gautam = 36 + 10 = 46 years
Hence, in year 2016, Gautam‘s age will not be thrice of his son‘s age.
Hence, option (b) is incorrect.
(c)
In year 2016, i.e. after 6 years from 2010:
Gautam‘s son‘s age = 8 + 6 = 14 years and its thrice value = 42 years
∴ After 6 years, age of Gautam = 36 + 6 = 42 years
Hence, in year 2016, Gautam‘s age will be thrice of his son‘s age.
Hence, option (c) is correct.
Incorrect
Answer: Option (c)
Explanation:
Present age of Gautam = 36 years
His son‘s age = 8 years
We will solve this by options.
(a)
In year 2014, i.e. after 4 years from 2010:
Gautam‘s son‘s age = 8 + 4 = 12 years and its thrice value = 36 years
∴ After 4 years, age of Gautam = 36 + 4 = 40 years
Hence, in year 2014, Gautam‘s age will not be thrice of his son‘s age.
Hence, option (a) is incorrect.
(b)
In year 2020, i.e. after 10 years from 2010:
Gautam‘s son‘s age = 8 + 10 = 18 years and its thrice value = 54 years
∴ After 10 years, age of Gautam = 36 + 10 = 46 years
Hence, in year 2016, Gautam‘s age will not be thrice of his son‘s age.
Hence, option (b) is incorrect.
(c)
In year 2016, i.e. after 6 years from 2010:
Gautam‘s son‘s age = 8 + 6 = 14 years and its thrice value = 42 years
∴ After 6 years, age of Gautam = 36 + 6 = 42 years
Hence, in year 2016, Gautam‘s age will be thrice of his son‘s age.
Hence, option (c) is correct.
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Question 4 of 5
4. Question
Raghav told to his son, “At the time of your birth, I was as old as you are today”. If Raghav is 38 years old today, what was his son’s age five years ago?
Correct
Answer: Option (a)
Explanation:
Raghav is 38 years old now. Let the age of son be x years today.
Age of Raghav when the son was born = Age of the son today = x years.
Raghav’s age today = Raghav’s age when the son was born + Age of son
So, 38 = x + x = 2x
Therefore, x =19 years
Age of son today = 19 years.
Age of son five years ago = 19 – 5 = 14 years
Hence, option (a) is the correct answer.
Incorrect
Answer: Option (a)
Explanation:
Raghav is 38 years old now. Let the age of son be x years today.
Age of Raghav when the son was born = Age of the son today = x years.
Raghav’s age today = Raghav’s age when the son was born + Age of son
So, 38 = x + x = 2x
Therefore, x =19 years
Age of son today = 19 years.
Age of son five years ago = 19 – 5 = 14 years
Hence, option (a) is the correct answer.
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Question 5 of 5
5. Question
Two statements S1 and S2 are given below followed by a question.
S1. The age difference between them is 6 years.
S2. The product of their ages is divisible by 6.
Question: What are the ages of two individuals, X and Y?
Correct
Answer: Option (d)
Explanation:
Statement 1 implies X – Y = 6.
Statement 2 implies XY is divisible by 6.
You can see that many values of X and Y can satisfy statement 1 and 2. Hence we can not get the exact values if X and Y . So option d is correct answer.
Incorrect
Answer: Option (d)
Explanation:
Statement 1 implies X – Y = 6.
Statement 2 implies XY is divisible by 6.
You can see that many values of X and Y can satisfy statement 1 and 2. Hence we can not get the exact values if X and Y . So option d is correct answer.
