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If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then A and C will be in the ratio
- a)3:13
- b)9:13
- c)36:13
- d)13:9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then ...
9 : 13
(A/B) × (B/C) = (3/4) × (12/13);
Or, A/B= 36/39= 9 : 13.
(A/B) × (B/C) = (3/4) × (12/13);
Or, A/B= 36/39= 9 : 13.
Most Upvoted Answer
If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then ...
Given:
A:B = 3:4
B:C = 12:13
To Find:
Ratio of A:C
Solution:
To find the ratio of A:C, we need to find the equivalent ratios of A:B and B:C such that we can cancel out the common term B.
Step 1: Find equivalent ratios of A:B and B:C
Since A:B = 3:4, we can multiply both sides by a common factor to find equivalent ratios. Let's choose the common factor as 12 (the denominator of B:C ratio).
A:B = 3:4
Multiply both sides by 12:
12A:12B = 36:48
Similarly, since B:C = 12:13, we can multiply both sides by a common factor to find equivalent ratios. Let's choose the common factor as 4 (the denominator of A:B ratio).
B:C = 12:13
Multiply both sides by 4:
4B:4C = 48:52
Step 2: Cancel out the common term B
We can cancel out the common term B by multiplying the A:B ratio by 4 and the B:C ratio by 12.
Multiply the A:B ratio (12A:12B) by 4:
4(12A:12B) = 4(36:48)
48A:48B = 144:192
Multiply the B:C ratio (4B:4C) by 12:
12(4B:4C) = 12(48:52)
48B:48C = 576:624
Step 3: Simplify the ratios
Now we have the ratios 48A:48B and 48B:48C. We can simplify these ratios by dividing both sides by 48.
48A:48B ÷ 48 = 144:192 ÷ 48
A:B = 3:4
48B:48C ÷ 48 = 576:624 ÷ 48
B:C = 12:13
Step 4: Find the ratio of A:C
Now that we have the ratios A:B = 3:4 and B:C = 12:13, we can multiply these ratios to find the ratio of A:C.
(A:B) × (B:C) = (3:4) × (12:13)
A:C = 36:52
Final Answer:
The ratio of A:C is 36:52, which can be simplified to 9:13. Therefore, the correct answer is option B, 9:13.
A:B = 3:4
B:C = 12:13
To Find:
Ratio of A:C
Solution:
To find the ratio of A:C, we need to find the equivalent ratios of A:B and B:C such that we can cancel out the common term B.
Step 1: Find equivalent ratios of A:B and B:C
Since A:B = 3:4, we can multiply both sides by a common factor to find equivalent ratios. Let's choose the common factor as 12 (the denominator of B:C ratio).
A:B = 3:4
Multiply both sides by 12:
12A:12B = 36:48
Similarly, since B:C = 12:13, we can multiply both sides by a common factor to find equivalent ratios. Let's choose the common factor as 4 (the denominator of A:B ratio).
B:C = 12:13
Multiply both sides by 4:
4B:4C = 48:52
Step 2: Cancel out the common term B
We can cancel out the common term B by multiplying the A:B ratio by 4 and the B:C ratio by 12.
Multiply the A:B ratio (12A:12B) by 4:
4(12A:12B) = 4(36:48)
48A:48B = 144:192
Multiply the B:C ratio (4B:4C) by 12:
12(4B:4C) = 12(48:52)
48B:48C = 576:624
Step 3: Simplify the ratios
Now we have the ratios 48A:48B and 48B:48C. We can simplify these ratios by dividing both sides by 48.
48A:48B ÷ 48 = 144:192 ÷ 48
A:B = 3:4
48B:48C ÷ 48 = 576:624 ÷ 48
B:C = 12:13
Step 4: Find the ratio of A:C
Now that we have the ratios A:B = 3:4 and B:C = 12:13, we can multiply these ratios to find the ratio of A:C.
(A:B) × (B:C) = (3:4) × (12:13)
A:C = 36:52
Final Answer:
The ratio of A:C is 36:52, which can be simplified to 9:13. Therefore, the correct answer is option B, 9:13.
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