Olympiad Test : Problems On Ages - Class 6 MCQ

Let the present ages of Sameer and Anand be
5x years and 4x years respectively.

⇒ 9(5x + 3) = 11(4x + 3)
⇒ 45x + 27 = 44x + 33
⇒ 45x – 44x = 33 – 27
⇒ x = 6
∴ Anand’s present age = 4x = 4 × 6 = 24 years.

Let C’s age be x years. Then, B’s age
= 2x years. A’s age = (2x + 2) years.
∴ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5 Hence, B’s age = 2x = 2 × 5 = 10 years.

Let the son’s present age be x years. Then,
(38 – x) = x
⇒ 2x = 38
⇒ x = 19
∴ Son’s age 5 years back = (19 – 5) = 14 years

Let the ages of children be x, (x + 3), (x + 6),
(x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4
∴ Age of the youngest child = x = 4 years.

Let Ronit’s present age be x years.
Then, father’s present age = (x + 3x) years = 4x years.
∴ (4x + 8) = 5/2(x + 8)
⇒ 8x + 16 = 5x + 40
⇒ 3x = 24
⇒ x = 8
Hence, required ratio = (4x + 16)/ (x + 16) = 48/24 = 2

Let the ages of father and son 10 years ago be 3x and years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio = (3x + 10) : (x + 10)
= 70 : 30 = 7 : 3.

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.

Let the mother’s present age be x years.
Then, the person’s present age = 2x/5 years.
∴ (2x/5 + 8) = 1/2 (x +8)
⇒ 2(2x + 40) = 5(x + 8)
⇒ x = 40

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.
∴ Required difference = (42 – 36) years  = 6 years

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
⇒ 20x = 80
⇒ x = 4
∴ Their present ages are 4x = 16 years,
7x = 28 years and 9x = 36 years respectively.

Let the son’s present age be x years.
Then, man’s present age = (x + 24) years.
∴ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then, (6x + 6) + 4 = 11
(5x + 6) + 4 = 10
⇒ 10(6x + 10) = 11(5x + 10)
⇒ 5x = 10
⇒ x = 2
∴ Sagar’s present age = (5x + 6) = 16 years.

Let the present ages of son and father be x and (60 – x) years respectively.
Then, (60 – x) – 6 = 5(x – 6)
⇒ 54 – x = 5x – 30
⇒ 6x = 84
⇒ x = 14
∴ Son’s age after 6 years = (x + 6) = 20 years.

Let the present ages of Arun and Deepak be
4x years and 3x years respectively. Then,
4x + 6 = 26  4x = 20
⇒ x = 5
∴ Deepak’s age = 3x = 15 years.

Let Rahul’s age be x years.
Then, Sachin’s age = (x – 7) years.
∴ (x – 7) / x = 7/9
⇒ 9x – 63 = 7x
⇒ 2x = 63
⇒ x = 31.5
Hence, Sachin’s age = (x – 7) = 24.5 years.

Let the ratio of their proportionality be x.
Then,
4x × x = 196
⇒ 4x² = 196
⇒ x = 7
Thus, father’s age = 28 years and son’s age = 7 years
After 5 years, father’s age = 33 years and son’s age = 12 years
∴ Ratio =33 : 12 = 11 : 4

Difference in ratios = 8
Then 8 ≡ 24
∴ 1 ≡ 3
Thus, value of 1 in ratio is equivalent to 3 years.
Thus, Rita’s age = 3 × 3 = 9 years
Mother’s age = 11 × 3 = 33 years
After 3 years, the ratio = 12 : 36 = 1 : 3

Let the age of the daughter be x years.
Then, the age of the mother is (50 – x) years
5 years ago, 7(x – 5) = 50 – x – 5
or, 8x = 50 – 5 + 35 = 80
∴ x = 10
Therefore, daughter’s age = 10 years and mother’s age = 40 years.

Let the age of the son be x years.
Then, the age of the father is (56 – x) years
After 4 years, 3(x + 4) = 56 – x + 4 or,
4x = 56 + 4 – 12 = 48
∴ x = 12 years Thus, son’s age = 12 years

Daughter’s age