Three numbers are in the ratio 3 : 2 : 5. The sum of their squares is 1862. Find the numbers. · ABC26GN1634
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: R.R.B. 2007
Three numbers are in the ratio 3 : 2 : 5. The sum of their squares is 1862. Find the numbers.
Answer
No answer key was printed for this question.
Explanation
Let the numbers be $3x, 2x$ and $5x$. Then, $(3x)^{2}+(2x)^{2}+(5x)^{2}=1862 \Rightarrow 9x^{2}+4x^{2}+25x^{2}=1862 \Rightarrow 38x^{2}=1862 \Rightarrow x^{2}=\frac{1862}{38}=49 \Rightarrow x=\sqrt{49}=7$. Hence, the numbers are 21, 14 and 35.
Explanation as extracted from the printed page; notation may be imperfect.