after 10 years age of Chandra Sahithi will be half of her mother 5years will be 20 more than three times of present age sahithi then find the present age of sahithi and her mother
Answers
Step-by-step explanation:
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The correct question is : After 10 years, age of Sahithi will be half of her mother's age 5 years ago and age of her mother after 5 years will be 20 more than three times the present age of Sahithi. Find the present ages of Sahithi and her mother, Chandra.
To find :
The present ages of Sahithi and her mother, Chandra.
Solution :
• Let the present age of Chandra be x, and that of Sahithi be y.
• Age of Chandra after 10 years will be x + 10.
Age of Chandra before 5 years was x - 5.
Age of Sahithi after 10 years will be y + 10.
• It is said that Sahithi's age after 10 years will be equal to half of her mother's age 5 years ago.
∴ According to the question,
y + 10 = ( x - 5 ) / 2
=> 2 ( y + 10 ) = x - 5
=> 2y + 20 = x - 5
=> x - 2y - 5 - 20 = 0
=> x - 2y - 25 = 0
=> x - 2y = 25 -(i)
• Age of Chandra after 5 years will be x + 5.
• Three times the present age of Sahithi = 3y
20 more than 3y = 20 + 3y
• According to the question,
x + 5 = 20 + 3y
=> x - 3y = 20 - 5
=> x - 3y = 15 -(ii)
• Subtracting equation (ii) from (i), we get;
(x - 2y) - (x - 3y) = 25 - 15
=> x - 2y - x + 3y = 10
=> - 2y + 3y = 10
=> y = 10
• Putting y as 10 in equation (i), we get;
x - 2× 10 = 25
=> x - 20 = 25
=> x = 25 + 20
=> 45
Therefore, the present age of Chandra is 45 years, and the present age of her daughter, Sahithi is 10 years.