Question 1
Answer
Question 1
The ages of the two persons differ by 16 years. If 6 years ago, the elder one by 3 times as old as the younger one, find their present ages.
Answer
Difference of present age for 2 Persons: 16 Years
6 Years ago, Elder age = 3 * younger age
Present ages =?
Let us assume the age of Person1 as x years
As the difference between Person1 and Person2 is 16 years
Person2 age = Person1 age – 16
Person2 age = x – 16
So Person1 is elder and Person2 is Younger.
6 Years ago:
Person1 age = x – 6
Person2 age = (x – 16 ) – 6 = x – 22
It is given that 6 Years ago, Elder age = 3 * younger age
x – 6 = 3 (x – 22)
x – 6 = 3x – 66
2x = 60
x = 30
Person1 Present age = x = 30 Years
Person2 Present age = x – 16 = 30 – 16 = 14 Years.
Note: You can cross-check your answer.
Like present ages 30 and 14. So 6 years before, ages would be 24 and 8.
So elder was 3 times of younger. So our answer is correct.
Answer is Present ages of Persons are 30 Years and 14 Years
Question 2
Answer
Question 2
The product of ages of Ankit and Nikita is 240. If twice age of Nikita is more than Ankit’s age by 4 years, what is Nikita’s age?
Answer
Age of Ankit * Age of Nikita = 240
2 * age of Nikita = Age of Ankit + 4
Nikita Age =?
Let us assume age of Nikita is x years and age of Ankit is y years.
As it is given: 2 * age of Nikita = Age of Ankit + 4
2x = y + 4
y = 2x – 4
Age of Ankit * Age of Nikita = 240
y * x = 240
(2x – 4) x = 240
2(x^2) – 4x – 240 = 0
x^2 – 2x – 120 = 0
x^2 – 12x + 10x – 120 = 0
x(x – 12) + 10(x – 12) = 0
(x + 10)(x – 12) = 0
So x + 10 = 0 or x – 12 = 0
x = -10 or x = 12
We need to ignore -10 and consider x = 12
Nikita present age = 12 years
Answer is Nikita’s age is 12 Years
Question 3
Answer
Question 3
Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their present ages?
Answer
8 Years ago: Rohit’s age = 4 * Son’s age
After 8 year: Rohit’s age = 2 * Son’s age
Let us assume the Present age of Rohit as x years and the present age of his son as y years
8 years ago:
Rohit’s age = x + 8 years
Son’s age = y + 8
Looking at given : 8 Years ago : Rohit’s age = 4 * Son’s age
x – 8 = 4 * (y – 8)
x – 8 = 4y – 32
x – 4y = – 24 ————————————–Equation1
After 8 Years:
Rohit’s age = x + 8 years
Son’s age = y + 8
Looking at given : After 8 year: Rohit’s age = 2 * Son’s age
x + 8 = 2 * (y + 8)
x + 8 = 2y + 16
x – 2y = 8 ——————————————Equation2
x – 4y = – 24 ————–Equation1
-x – 2y = 8 —————Equation2
Solving Equation1 & Equation2:
-2y = -32
y = 16 [Present age of Son]
Put value of y in Equation1
x – 4y = – 24
x – (4 * 16) = -24
x – 64 = -24
x = 40 [Present age of Rohit].
The answer is Present age of Rohit is 40 Years and the Present age of the son is 16 years
Question 4
Answer
Question 4
One year ago, the ratio of Gaurav’s and Sachin’s ages was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Sachin?
Answer
1 Year ago Gaurav Age : Sachin age = 6 : 7
4 Years hence, Gaurav Age : Sachin age = 7 : 8
Sachin’s Age = ?
Let us assume Gaurav’s present age as x years and present age of Sachin as y years.
1 Year ago:
Gaurav’s age = x – 1 years
Sachin’s age = y – 1 years
As per Given: 1 Year ago Gaurav Age : Sachin age = 6 : 7
(x-1)/(y-1) = 6/7
7(x -1 ) = 6 (y -1)
7x – 7 = 6y – 6
7x – 6y = 1 ————————–Equation1
Four years hence:
Gaurav’s age = x + 4 years
Sachin’s age = y + 4 years
As per Given: 4 Years hence, Gaurav Age : Sachin age = 7 : 8
(x+4)/(y+4) = 7/8
8x + 32 = 7y + 28
8x – 7y = – 4 ————————–Equation2
We can not solve Equation1 and Equation2 directly as nothing is common to cancel
We will multiply Equation1 by 8 and Equation2 by 7
Equation1 : 7x – 6y = 1 [Multiply by 8 both sides]
56x – 48y = 8 —————–Equation3
Equation2 : 8x – 7y = -4 [Multiply by 7 both sides]
56x – 49y = -28 ——————Equation4
56x – 48y = 8
– 56x – 49y = – 28
y = 36
Answer is Sachin’s present age is 36 years
Question 5
Answer
Question 5
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
The present age of Arun : Present age of Deepak = 4 : 3
After 6 years Arun’s age = 26 Years
Deepak’s Present age =?
After 6 years Arun’s age will be 26 years.
So at Present Arun’s age = 26 – 6 = 20 years
Given that the Present age ratio Arun : Deepak = 4 : 3
(Present Age of Arun / Present Age of Deepak) = 4/3
20 / Present Age of Deepak = 4/3
Present Age of Deepak = 20*3/4 = 15 Years
The answer is Deepak’s Present age is 15 years.
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Question 6
Answer
Question 6
Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was their ratio 3:5?
a) 5 years
b) 10 years
c) 20 years
d) 37 years
Answer
In such kind of scenario, it is always better to go with options rather than solve questions.
How many years ago the ratio was 3 : 5?
Hitesh present age = 40 years
Ronnie present age = 60 years
Option a: 5 years
5 years ago Hitesh age = 40 – 5 = 35
5 years ago Ronnie age = 60 – 5 = 55
35 : 55 = 7 : 11 [So a is not answer]
Option b: 10 years
10 years ago Hitesh age = 40 – 10 = 30
10 years ago Ronnie age = 60 – 10 = 50
30 : 50 = 3 : 5 [As it is matching with our expectation as 3: 5 ,so it is correct answer]
Answer is 10 Years ago ratio of Hitesh and Ronnie’s age was 3 : 5
Question 7
Answer
Question 7
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of Son is?
Answer
Man present age = Son’s present age + 24
After 2 years, Man’s age = 2 * son’s age
Present age son =?
Let us assume the present age of the son is x years.
Man’s Present age = x +24
After 2 years:
Son age = x + 2
Man age = 2 (x + 2) = 2x + 4 ———Equation1
However Man’s age after 2 years will be (x + 24) + 2= x +26 ———–Equation2
Equation1 and Equation2 both are equal and nothing but man’s age after 2 years
2x + 4 = x + 26
x = 22 [Present age of son]
Answer is Present age of Son is 22 years
Question 8
Answer
Question 8
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 age + B age = B age + C age + 12
C how many years younger = ?
Assume A age: A years, B: B years, and C: C years
It is given that:
A + B = B + C + 12
A = C + 12
This means C is 12 years younger than A.
The answer is C is 12 years younger than A
Question 9
Answer
Question 9
The sum of ages of the father and his son is 45 Years. Five years ago, the product of their age was 34 years. What are the ages of son and father respectively?
Answer
Present Father age + Son age = 45 years
5 years ago product of ages = 34
The present age of Father’s age and Son’s age = ?
Here we can take the 2nd part to solve the problem quickly.
5 years ago product of ages = 34
As to getting product 34 there are only two options:
1) 17 * 2
2) 34 * 1
Let us take Option 1 :
5 years ago Father’s age 17 and Son age 2
So present age Father’s age = 17 + 5 = 22
Present age Son = 2 + 5 = 7
Total of 22 and 7 is not 45
Option 2
5 years ago Father’s age 34 and Son age 1
So present age Father’s age = 34 + 5 = 39
Present age Son = 1 + 5 = 6
Total of 39 and 6 is 45
The answer is the Present age of the Father 39 Years and Son age is 6 years.
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