Question

Three numbers are in the ratio 1/3:1/5:1/6. If the sum of their squares is 664, find the numbers

Answer 1

Correct question:-

Three numbers are in the ratio 1/3:1/5:1/6. If the sum of their squares is 644, find the numbers.

Given:-

• Ratio of three numbers = 1/3 : 1/5 : 1/6
• Sum of their squares = 644

To find:-

• The three numbers

Answer:-

Given ratio of three numbers = 1/3 : 1/5 : 1/6

First we have to convert the ratio which is in the form of fractions, to the form of whole numbers.

We know that, the ratio remains the same on multiplying or dividing the whole ratio by a number.

So, here we will multiply the whole ratio by LCM of the denominators of the fractions, i.e., LCM of 3, 5, 6

LCM of 3, 5, 6 = 30

So, multiplying entire ratio with 30,

1/3 : 1/5 : 1/6 = 30 * (1/3 : 1/5 : 1/6)

→ 1/3 : 1/5 : 1/6 = 30/3 : 30/5 : 30/6

→ 1/3 : 1/5 : 1/6 = 10 : 6 : 5

The ratio is now in the form of whole numbers.

Now, accroding tot he given ratio, let the numbers be 10x, 6x, and 5x

According to the question,

(10x)² + (6x)² + (5x)² = 644

→ 100x² + 36x² + 25x² = 644

→ 161x² = 644

→ x² = 4

→ x = ±2

If x = +2,

• 1st number = 10x = (10 * 2) = 20
• 2nd number = 6x = (6 * 2) = 12
• 3rd number = 5x = (5 * 2) = 10

If x = -2,

• 1st number = 10x = (10 * -2) = -20
• 2nd number = 6x = (6 * -2) = -12
• 3rd number = 5x = (5 * -2) = -10