Advertisements
Advertisements
प्रश्न
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Advertisements
उत्तर
Let one of the number be x then other number is (18 - x).
Then according to question,
`1/x+1/(18-x)=1/4`
`rArr(18 - x+x)/(x(18-x))=1/4`
⇒ 18 x 4 = 18x - x2
⇒ 72 = 18x - x2
⇒ x2 - 18x + 72 = 0
⇒ x2 -12x - 6x + 72 = 0
⇒ x(x - 12) - 6(x - 12) = 0
⇒ (x - 6)(x - 12) = 0
⇒ x - 6 = 0
⇒ x = 6
Or
⇒ x - 12 = 0
⇒ x = 12
Since, x being a number,
Therefore,
When x = 12 then another number will be
18 - x = 18 - 12 = 6
And when x = 6 then another number will be
18 - x = 18 - 6 = 12
Thus, the two numbers are 6 and 12.
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
The sum of a numbers and its positive square root is 6/25. Find the numbers.
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
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.
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
A two digit number is four times the sum and 3 times the product of its digits, find the number.
Solve equation using factorisation method:
x(x – 5) = 24
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
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.
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
