Advertisements
Advertisements
Question
Three positive numbers are in the ratio `1/2 : 1/3 : 1/4`. Find the numbers if the sum of their squares is 244.
Solution
Given, three positive numbers are in the ratio `1/2 : 1/3 : 1/4 = 6 : 4 : 3`
Let the numbers be 6x, 4x and 3x.
From the given information,
(6x)2 + (4x)2 + (3x)2 = 244
36x2 + 16x2 + 9x2 = 244
61x2 = 244
x2 = 4
x = ± 2
Since, the numbers are positive, so x = 2.
Thus, the numbers are 12, 8 and 6.
APPEARS IN
RELATED QUESTIONS
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
The sum of a number and its reciprocal is 4.25. Find the number.
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.
Divide 15 into two parts such that the sum of their reciprocals is `3/10`.
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.
In a two-digit number, the ten’s digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.
The product of two consecutive even whole numbers is 24, the numbers are ______.
The sum of a number and its reciprocal is 5.2. The number is ______.
The difference between the digits of a two-digit number is 2 and the product of digits is 24. If tens digit is bigger, the number is ______.
