Question

three numbers are in the ratio 2 is to 3 is to 5 if the difference of the cube of the third and the first number is 25272 then the difference in squares of first and the second number is​

Answer 1

GIVEN :-

• Three numbers are in ratio 2:3:5.
• Difference between cube of 3rd and 1st number is 25272.

TO FIND :-

• Difference between squares of 1st and 2nd number.

SOLUTION :-

The three numbers are in ratio . So, there must be a common multiple, let 'x'.

Numbers are :-

• 1st number = 2x
• 2nd number = 3x
• 3rd number = 5x

♦ Difference between cube of 3rd and 1st number is 25272.

→ (5x)³ - (2x)³ = 25272

→ 125x³ - 8x³ = 25272

→ 117x³ = 25272

→ x³ = 25272/117

→ x³ = 216

→ x = ³√216

→ x = 6

Numbers are :-

• 1st number = 2x = 2(6) = 12
• 2nd number = 3x = 3(6) = 18
• 3rd number = 5x = 5(6) = 30

Now , we will find difference between square of 1st and 2nd number.

12² - 18² = 144 - 324 = -180

Hence , difference between squares of 1st and 2nd number is -180.