Mathematics
Four years ago Marina was three times old as her daughter. Six years from now the mother will be twice as old as her daughter. Find their present ages.
Linear Equations
82 Likes
Answer
Let present age of Marina be x years and daughter's age be y years.
Four years ago,
Age of Marina = (x - 4) years
Age of Marina's daughter = (y - 4) years
According to first condition in the problem,
⇒ (x - 4) = 3(y - 4)
⇒ x - 4 = 3y - 12
⇒ 3y - x = 8 …….(i)
After 6 years,
Age of Marina = (x + 6) years
Age of Marina's daughter = (y + 6) years
According to second condition in the problem,
⇒ x + 6 = 2(y + 6)
⇒ x + 6 = 2y + 12
⇒ x - 2y = 6 …….(ii)
Adding eq. (i) and (ii) we get,
⇒ (3y - x) + (x - 2y) = 8 + 6
⇒ 3y - 2y - x + x = 14
⇒ y = 14.
On substituting value of y in (ii) we get,
⇒ x - 2(14) = 6
⇒ x - 28 = 6
⇒ x = 34.
Hence, present age of Marina = 34 years and daughter = 14 years.
Answered By
33 Likes
Related Questions
The result of dividing a number of two digits by the number with the digits reversed is . If the difference of digits is 1, find the number.
A number of three digits has the hundred digit 4 times the unit digit and the sum of three digits is 14. If the three digits are written in the reverse order, the value of the number is decreased by 594. Find the number.
On selling a tea set at 5% loss and a lemon set at 15% gain, a shopkeeper gains ₹70. If he sells the tea set at 5% gain and lemon set at 10% gain he gains ₹130. Find the cost price of lemon set.
A person invested some money at 12% simple interest and some other amount at 10% simple interest. He received yearly interest of ₹1300. If he had interchanged the amounts, he would have received ₹40 more as yearly interest. How much did he invest at different rates?