The three numbers A, B, C are in the ratio
2
1
:
3
2
:
4
3
. The difference between greatest and smallest numbers is 21. The three numbers A, B and C respectively are:
- A56, 42, 63
- B63, 56, 42
- C42, 63, 56
- D42, 56, 63
Solution & Step-by-step Explanation
The given ratio is:
A:B:C=
2
1
:
3
2
:
4
3
To convert this into a whole number ratio, multiply each term by the LCM of denominators (2,3,4), which is 12:
A=
2
1
×12=6
B=
3
2
×12=8
C=
4
3
×12=9
So, A:B:C=6:8:9.
Let the numbers be 6x, 8x, and 9x.
The greatest number is 9x and the smallest number is 6x.
Given difference:
9x−6x=21
3x=21⟹x=7
Now, calculate the three numbers:
A=6×7=42
B=8×7=56
C=9×7=63
Thus, the numbers are 42,56,63.
A:B:C=
2
1
:
3
2
:
4
3
To convert this into a whole number ratio, multiply each term by the LCM of denominators (2,3,4), which is 12:
A=
2
1
×12=6
B=
3
2
×12=8
C=
4
3
×12=9
So, A:B:C=6:8:9.
Let the numbers be 6x, 8x, and 9x.
The greatest number is 9x and the smallest number is 6x.
Given difference:
9x−6x=21
3x=21⟹x=7
Now, calculate the three numbers:
A=6×7=42
B=8×7=56
C=9×7=63
Thus, the numbers are 42,56,63.