Mathematics
Three years hence a man's age will be three times his son's age, and 7 years ago he was seven times as old as his son. How old are they now?
Answer
Let present age of son be x and man's age be y.
According to first condition,
⇒ (y + 3) = 3(x + 3)
⇒ y + 3 = 3x + 9
⇒ y - 3x = 9 - 3
⇒ y - 3x = 6 ……(i)
According to second condition,
⇒ (y - 7) = 7(x - 7)
⇒ y - 7 = 7x - 49
⇒ y - 7x = -49 + 7
⇒ y - 7x = -42
⇒ 7x - y = 42 ……(ii)
Adding (i) and (ii) we get,
⇒ y - 3x + 7x - y = 6 + 42
⇒ 4x = 48
⇒ x = 12.
Substituting value of x in (i) we get,
⇒ y - 3(12) = 6
⇒ y - 36 = 6
⇒ y = 42.
Hence, son's age = 12 years and man's age = 42 years.
Related Questions
Shikha works in a factory. In one week she earned ₹ 3,900 for working 47 hours, of which 7 hours were overtime. The next week she earned ₹ 4,160 for working 50 hours, of which 8 hours were overtime. What is Shikha's hourly earning rate?
The sum of digits of a two digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the number.
Rectangles are drawn on line segments of fixed lengths. When the breadths are 6m and 5m respectively the sum of the areas of the rectangles is 83 m2. But if the breadths are 5m and 4m respectively the sum of the areas is 68 m2. Find the sum of the areas of squares drawn on the line segments.
If the length and breadth of a room are increased by 1 metre each, the area is increased by 21 square meters. If the length is decreased by 1 meter and the breadth is increased by 2 meters, the area is increased by 14 square meters. Find the perimeter of the room.