Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the present age of girl be x years then, age of her sister x/2 years
Then, 4 years later, age of girl (x + 4) years and her sister’s age be `(x/2+4)Years`
Then according to question,
`(x+4)(x/2+4)=160`
(x + 4)(x + 8) = 160 x 2
x2 + 8x + 4x + 32 = 320
x2 + 12x + 32 - 320 = 0
x2 + 12x - 288 = 0
x2 - 12x + 24x - 288 = 0
x(x - 12) + 24(x - 12) = 0
(x - 12)(x + 24) = 0
So, either
x - 12 = 0
x = 12
Or
x + 24 = 0
x = -24
But the age never be negative
Therefore, when x = 12 then
`x/2=12/2=6`
Hence, the present age of girl be 12 years and her sister’s age be 6 years.
APPEARS IN
संबंधित प्रश्न
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Solve the following quadratic equations by factorization:
`x^2-(sqrt2+1)x+sqrt2=0`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
Find the consecutive numbers whose squares have the sum 85.
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
