1. If A: B=1:2, B: C= 3:4,C: D= 6: 9 and
D: E = 12:16, then A:B:C:D: E equal to
Answers
Answer:
A:B=1:2
B:C=3:4
C:D=6:9
D:E=12:16
For understanding it in steps , I’ll first explain calculating A:B:C, ensuring you are understanding it clearly.
Write A:B:C as A:B,B:C: here 1:2,3:4. Say 1:2 is the first expression and 3:4 is the second expression. Maintain the ratios of both expressions and multiply both the expressions such that the 2nd term of the first expression and 1st term of the second expression is constant. You can multiply them until those terms become the LCM. The expressions are 3:6,6:8. Therefore, A:B:C=3:6:8
If that sounds too theoretical to understand:
A:B=1:2. B:C=3:4. B is common here. And has different values. To make it the same, take LCM and hold the ratios making the value of B equal to the LCM.
Here, LCM of 2 and 3 is 6. So A:B becomes 3:6 - (1:2)X3 [multiplied by 3 because B has to be 6(LCM)] and B:C becomes 6:8 - (3:4)X2. [multiplied by 2 because B has to be 6(LCM)]
Therefore A:B:C=3:6:8
Similarly, A:B:C=3:6:8, C:D=6:9. LCM of 8 and 6 is 24.
Therefore A:B:C=9:18:24 and C:D=24:36
Implying, A:B:C:D=9:18:24:36
Now, A:B:C:D=9:18:24:36 can be simplified to 3:6:8:12 as the numbers are too big for them to be used next time. We get the same results even if we do not simplify them. D:E=12:16. And surprisingly, A:B:C:D when simplified is 3:6:8:12.
A:B:C:D=3:6:8:12 and D:E=12:16.
Therefore, A:B:C:D:E=3:6:8:12:16.
Hope you understood. :)