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Problems on Age - (Page -4)

Problems on Age - (Page -4)

25.If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18, then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay 's present age?

**Answer : Option B**

**Explanation :**

Present age of Denis = 5 years

Present age of Rahul = 5-2 = 3

Let the present age of Ajay = x

Then (x-6)/18 = present age of Rahul = 3

=> x- 6 = 3×18 = 54

=> x = 54 + 6= 60

26.The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married

=> x = 54 + 6= 60

26.The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married

A.8 B.10
C. 11 D.12

**Answer : Option D**

**Explanation :**

Let
the present age of the man and his wife be 4x and 3x respectively.

After
4 years this ratio will become 9:7

=>
(4x + 4)/ (3x + 4) = 9/7

=>
28x + 28 = 27x + 36

=>
x = 8

=>
Present age of the man = 4x = 4×8 = 32

Present
age of his wife = 3x = 3×8 = 24

Assume
that they got married before t years.

Then
(32 – t) / (24 – t) = 5/3

=>
96 – 3t = 120 – 5t

=>
2t = 24

=>
t = 24/2 = 12

27.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?

A.16 B.14
C. 12 D.10

**Answer : Option C**

**Explanation :**

Let
the age of Sunil = x and age of Syam = y.

Then
xy = 240 ---(1) 2x = y + 4

=>
y = 2x – 4

=>
y = 2(x – 2) ---(2)

Substituting
equation (2) in equation (1). We get x × 2(x-2) = 240

=>
x (x-2) = 240/2

=>
x (x -2) = 120 ---(3)

We
got a quadratic equation to solve. Always time is precious
and objective tests measures not only how accurate
you are but also how fast you are. We can either
solve this quadratic equation in the traditional way. But more easy way is just
substitute the values given in the choices in the
quadratic equation (equation 3 ) and see which
choice satisfy the equation.

Here the 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

28.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?

A.32 B.34
C. 36 D.38

**Answer : Option C**

**Explanation :**

Let
take the age of Sooraj and Vimal , 1 year ago as 6x and 7x respectively. Given that, four years hence, this ratio would
become 7: 8.

=>
(6x + 5)/(7x + 5) = 7/8

=>
48x + 40 = 49x + 35

=>
x = 5

Vimal's
present age = 7x + 1 = 7×5 + 1 = 36

29.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?

A.10 B.11
C. 12 D.13

**Answer : Option C**

**Explanation :**

Given
that A+B = 12 + B + C

=>
A – C = 12 + B – B = 12

=>
C is younger than A by 12 years

30.Sachin's
age after 15 years will be 5 times his age 5 years back. Find out the present
age of Sachin?

A.10 B.11
C. 12 D.13

**Answer : Option A**

**Explanation :**

Let
the present age of Sachin = x

Then
(x+15) = 5(x-5)

=>
4x = 40

=>
x = 10

31.Sandeep's
age after six years will be three-seventh of his father's age. Ten years ago
the ratio of their ages was 1 : 5. What is Sandeep's father's age at present?

A.30 B.40 C. 50
D.60

**Answer : Option C**

**Explanation :**

Let
the age of Sandeep and his father before 10 years be x and 5x respectively. Given that Sandeep's age after six years will be
three-seventh of his father's age

=>
x + 16 = (3/7)(5x + 16)

=>
7x + 112 = 15x + 48

=>
8x = 64

=>
x = 8

Sandeep's
father's present age = 5x + 10 = 5×8 + 10 = 50

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