Correct option is D
Information Given:
Ratio of age of X ten years ago to Y six years ago = 2 : 3.
Ratio of age of X four years hence to Y six years hence = 5 : 6.
Asked: Difference between present ages of X and Y.
Concept/Formula Used:
Age ten years ago = Present age - 10.
Age six years ago = Present age - 6.
Age four years hence = Present age + 4.
Age six years hence = Present age + 6.
Use ratio expressions and solve algebraic equations to find present ages.
Explanation:
Let present age of X = x years and present age of Y = y years.
From first ratio:
(x - 10) / (y - 6) = 2 / 3
Cross multiply:
3(x - 10) = 2(y - 6)
3x - 30 = 2y - 12
3x - 2y = 18 ---- (1)
From second ratio:
(x + 4) / (y + 6) = 5 / 6
Cross multiply:
6(x + 4) = 5(y + 6)
6x + 24 = 5y + 30
6x - 5y = 6 ---- (2)
Multiply equation (1) by 5 and equation (2) by 2:
15x - 10y = 90 ---- (3)
12x - 10y = 12 ---- (4)
Subtract (4) from (3):
(15x - 12x) - (10y - 10y) = 90 - 12
3x = 78
x = 26
Substitute x = 26 into (1):
3(26) - 2y = 18
78 - 2y = 18
-2y = 18 - 78 = -60
2y = 60
y = 30
Difference between present ages:
y - x = 30 - 26 = 4 years.
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