The ratio of the current ages of Momen and... | গাণিতিক যুক্তি Multiple Choice Question

Question: The ratio of the current ages of Momen and his brother is 15:14. The ratio of the ages of Momen and his sister in 6 years will be 18:19. The gap between Momens age and his sister is the same as the gap between Momens age and his brother. What is Momens current age?

Solution:
Let's say Momen's current age is x
From the first ratio (Momen : Brother = 15 : 14) If Momen's age is x, then his brother's age is (14x/15)
Let's say Momen's sister's age is y

Given that the gap between Momen and sister is same as gap between Momen and brother
|x - y| = |x - (14x/15)|
|x - y| = |x - 14x/15|
|x - y| = |15x/15 - 14x/15|
|x - y| = x/15 ...... (1)

After 6 years, the ratio of Momen:Sister will be 18:19
(x + 6)/(y + 6) = 18/19
19(x + 6) = 18(y + 6)
19x + 114 = 18y + 108
19x = 18y - 6
y = (19x + 6)/18 .......... (2)

From equations 1 and 2 ⇒
x - y = x/15 (since y is less than x)
x - (19x + 6)/18 = x/15
18x - 19x - 6 = 18x/15
-x - 6 = 18x/15
-15x - 90 = 18x
-33x = 90
x = 30

Therefore, Momen's current age is 30 years.

The ratio of the current ages of Momen and his brother is 15:14. The ratio of the ages of Momen and his sister in 6 years will be 18:19. The gap between Momens age and his sister is the same as the gap between Momens age and his brother. What is Momens current age?

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