Sony is one-fifth the age of her mother 15 years ago and Sony’s brother is three-fifth the age of his mother 10 years ago. If the sum of Sony and her brother’s ages is 31 then how old is Sony's mother ?
A) 40 B) 50 C) 60 D) 70
Answers
☞ Your Answer is 50 years
☆ Age of Sonu's morher?
◕ Let the age of Mother br x
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Let the present age of Sony be x
the present age of her brother be y
the present age of her mother be z
By the given conditions,
x - 15 = 1/5 (z - 15)
5(x - 15) = z-15
5x - 75 = z - 15
z = 5x - 75 + 15
z = 5x - 60 ----------(1)
y - 10 = 3/5 (z - 10)
5(y - 10) = 3(z - 10)
5y - 50 = 3z - 30
5y = 3z + 20 ------------(2)
x + y = 31
x = 31 - y -------------(3)
Substituting (3) in (1)
z = 5(31 - y) - 60
z = 155 - 5y - 60
z = 95 - 5y --------------(4)
Substituting (2) in (4)
z = 95 - (3z + 20)
z = 95 - 3z - 20
3z + z = 75
4z = 75
z = 75/4 yrs
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