Two positive numbers are in the ratio 8: 13. If the sum of their squares is 2097, then the sum of the two numbers is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 63
Explanation:
Let the two numbers be 8x and 13x respectively.
According to the given question,
(8x)2 + (13x)2 = 2097
⇒ 64x2 + 169x2 = 2097
⇒ 233x2 = 2097
⇒ x2 = 9
⇒ x = 3
Now required sum = 8x + 13x = 21x = 21 × 3 = 63
Hence the required answer is 63.