Advertisements
Advertisements
प्रश्न
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Advertisements
उत्तर
Let the present age of the man be x years
Then present age of his son is (45 - x) years
Five years ago, man’s age = (x - 5) years
And his son’s age (45 - x - 5) = (40 - x) years
Then according to question,
(x - 5)(40 - x) = 4(x - 5)
40x - x2 + 5x - 200 = 4x - 20
-x2 + 45x - 200 = 4x - 20
-x2 + 45x - 200 - 4x + 20 = 0
-x2 + 41x - 180 = 0
x2 - 41x + 180 = 0
x2 - 36x - 5x + 180 = 0
x(x - 36) -5(x - 36) = 0
(x - 36)(x - 5) = 0
So, either
x - 36 = 0
x = 36
Or
x - 5 = 0
x = 5
But, the father’s age never be 5 years
Therefore, when x = 36 then
45 - x = 45 - 36 = 9
Hence, man’s present age is36 years and his son’s age is 9 years.
APPEARS IN
संबंधित प्रश्न
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
Two numbers differ by 3 and their product is 504. Find the number
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
Solve each of the following equations by factorization:
x(x – 5) = 24
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve equation using factorisation method:
(2x – 3)2 = 49
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Find two consecutive natural numbers such that the sum of their squares is 61.
Find three successive even natural numbers, the sum of whose squares is 308.
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
If `x + 1/x = 2.5`, the value of x is ______.
