If A - B - C - 2 - 3 - 4- then what is A-B - B-C - C-A equal to-

The correct option is C 8 : 9 : 24 Let A = 2k, B = 3k, C = 4k.Then, #160; A/B = 2k3k = 2/3 , BC = 3k/4k = 34, C/A = 4k2k = 21 ∴A/B : #160;B/C ...

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Byju's Answer

Standard VII

Mathematics

Changing Scale (Including Flags)

If A : B : ...

Question

If $A : B : C = 2 : 3 : 4,$ then what is $\frac{A}{B} : \frac{B}{C} : \frac{C}{A}$ equal to?

4 : 5 : 15

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3 : 7 : 18

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6 : 2 : 21

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8 : 9 : 24

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Solution

The correct option is C $8 : 9 : 24$
Let A = 2k, B = 3k, C = 4k.
Then,
$\frac{A}{B} = \frac{2 k}{3 k} = \frac{2}{3}, \frac{B}{C} = \frac{3 k}{4 k} = \frac{3}{4}, \frac{C}{A} = \frac{4 k}{2 k} = \frac{2}{1}$

$∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2}{3} : \frac{3}{4} : \frac{2}{1} (L C M = 12)$

Let A = 2k, B = 3k, C = 4k.

Then, $\frac{A}{B} = \frac{2 k}{3 k} = \frac{2}{3}, \frac{B}{C} = \frac{3 k}{4 k} = \frac{3}{4}, \frac{C}{A} = \frac{4 k}{2 k} = \frac{2}{1}$ $∴ \frac{A}{B} : \frac{B}{C} : \frac{C}{A} = \frac{2}{3} : \frac{3}{4} : \frac{2}{1} (L C M = 12)$

$= \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 = 8 : 9 : 24.$

$= \frac{2}{3} \times 12 : \frac{3}{4} \times 12 : \frac{2}{1} \times 12 = 8 : 9 : 24.$

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Q. If

a : b : c = 3 : 4 : 7

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If A = {3, 6, 9, 12, 15, 18, 21}
B = {2, 4, 6, 8, 10, 12, 14, 16}
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$\begin{matrix} A & B 1. B - C & A . {5, 10, 20} 2. A - C & B . {3, 9, 15, 21} 3. C - (A - B) & C . {3, 6, 9, 12, 18, 21} 4. C \cap (A - B) & D . {15} E . {2, 4, 6, 8, 12, 14, 16} \end{matrix}$

Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data:

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

Q. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} then prove the following :
A' = {5, 6, 7, 8, 9}

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28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

If A:B:C=2:3:4, then what is AB:BC:CA equal to?

The correct option is C 8:9:24Let A = 2k, B = 3k, C = 4k.Then, AB=2k3k=23,BC=3k4k=34,CA=4k2k=21∴AB:BC:CA=23:34:21(LCM=12)Let A = 2k, B = 3k, C = 4k.Then, AB=2k3k=23,BC=3k4k=34,CA=4k2k=21∴AB:BC:CA=23:34:21(LCM=12)=23×12:34×12:21×12=8:9:24.=23×12:34×12:21×12=8:9:24.

If $A : B : C = 2 : 3 : 4,$ then what is $\frac{A}{B} : \frac{B}{C} : \frac{C}{A}$ equal to?

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9