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
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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.
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