Math, asked by Krutik8733, 9 months ago

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

Answered by ExᴏᴛɪᴄExᴘʟᴏʀᴇƦ
46

\huge\sf\pink{Answer}

☞ Your Answer is 50 years

\rule{110}1

\huge\sf\gray{To \:Find}

☆ Age of Sonu's morher?

\rule{110}1

\huge\sf\purple{Steps}

◕ Let the age of Mother br x

\sf Sonu's \ Age = \dfrac{x-15}{5} \ years

\sf Brother's \ Age = \dfrac{3(x-10}{5} \ years

\bullet\underline{\textsf{ As Per the Question}}

\sf  \dfrac{x-15}{5} + \dfrac{(3x-30)}{5} = 31

\sf   x - 15 + 3x-30 = 31×5\\

\sf   4x - 45 = 115\\

\sf  4x = 200 \\

\sf  x = \frac{200}{4} \\

\sf\orange{x = 50 \ years}   \\

\rule{170}3

Answered by zahaansajid
47

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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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