Deloitte Problems on Ages Questions and Answers Quiz-1

Let us suppose Raman's current age to be = x years.

5 years back his age would have been = x - 5

15 years time his age will be = x + 15

So, his present age will be =

5(x- 5) = x + 15

5x - 25 = x + 15

4x =. 40

x = 10

So, his Current age is 10

Let Neha's present age be x years.

Her age 12 years ago = (x - 12) years

Therefore, her mothers age 12 years ago = 4(x - 12)

Her mothers present age = 4x - 48 + 12 = 4x - 36

Nehas age after 12 years = x + 12

Her mothers age after 12 years = 4x - 36 + 12 = 4x - 24

=> 4x - 24 = 2(x + 12)

=> 4x - 2x = 24 + 24

=> x = 24

Therefore, Nehas present age = 24

Hence, Her mothers present age = 4x - 36 = 4(24) - 36 = 60 years.

Video solution:

Let the ages of husband and wife at the time of their 20th wedding anniversary be X years and Y years respectively and X > Y.
Their combined age = (X + Y) years.
The ages of both husband and wife at the time of wedding will be (X – 20) years and (Y – 20) years respectively.
Their combined age = (X – 20) + (Y – 20)
= (X + Y – 40) Years
By first information, we have
(X + Y) = 2( X + Y – 40)
X + Y = 2X + 2Y - 80
Therefore, X + Y = 80-------A
and by second information, we have
X – Y =3 ----------------------B
Solving A and B, we get X = 41.5 years
Therefore, the age of husband at the time of their 20th wedding anniversary X = 41.5 years
Age at the time of marriage = 41.5 years – 20 years = 21.5 years.

Video solution:

Let the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then,
5x + 6 = 26
5x = 20
x = 4
Dhiraj’s age = 4x = 16 years

Video solution:

Total present age of the family 22\times 6 = 132 years
Total age of the family 7 years ago = (132 - 7\times 6 ) = 90 years
At that time, the number of member = 5
Therefore Average age at that time = \frac{90}{5}= 18 years

Video solution:

Average age of a family of 4 members was 19 years, 4 years back.

Let the ages of 4 members be a,b,c,d 4 years ago

19 = \frac{\text{Sum of all ages}}{4}

19 = \frac{a+b+c+d}{4}

19 \times 4 = {a+b+c+d}

76 = {a+b+c+d}

So, the sum of ages of 4 members 4 years ago is 76

Now after four years their ages will be increase by 4

So, the sum of ages of 4 members after 4 years = a+4+b+4+c+4+d+4

=a+b+c+d+16

= 76+16

= 92

Let the present age of baby be x

Sum of ages of 4 members and baby = 92+x

Now total members = 4+1=5

the average age of the family same even today.

So, 19 = \frac{92+x}{5}

19 \times 5 =92+x

95 =92+x

x=3

Hence The present age of child is 3 years.

Video solution:

Since its 13 years ago

Nina's 13 year ago age = Present age - 13 = 37 - 13 = 24

Aman 13 year ago age = Present age - 13 = 59 - 13 = 46

Ratio = \frac{24}{46} = 12:23

Video solution:

Total Age of 10 students and Teacher = 11 x 15 = 165

Total age of first 7 students = 7 x 15 = 105

Total age of 3 students = 3 x 11 = 33

Thus total age of students = 33 + 105 = 138

Age of Teacher = 165 - 138 = 27


Video solution:

At present

Age of Umesh = x

Age of Reena is Y age of Mahesh is m

after 6 years

X+6=4(y+6)

X+6=4y+24

But it is given that age of Mahesh is equal to 7 times age of Reena

So

7y+6=4y+24

3y+6=24

3y=18

Y=6

Age of Mahesh is equal to 7 times the age of Reena

X= 7\times 6

= 42

Video solution: