Question:
If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?
If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?
Updated On: Jul 29, 2025
- 201
- 205
- 207
- 210
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The Correct Option is C
Solution and Explanation
To solve the problem, we need to find a possible value of (a + b + c) given the ratio conditions.
1. From the problem, we know:
- Ratio of a:b is 3:4.
- Ratio of b:c is 2:1.
2. Introduce variables based on ratios:
- Let a = 3k, b = 4k (from the a:b ratio of 3:4).
- Let b = 2m, c = m (from the b:c ratio of 2:1).
3. Equate expressions for b to find k and m relation:
- 4k = 2m ⇒ m = 2k.
4. Express a, b, and c terms using k:
- a = 3k
- b = 4k
- c = m = 2k
5. Find the expression for a + b + c:
- a + b + c = 3k + 4k + 2k = 9k
6. Find a possible value of 9k matching given options.
7. Check the options to see which is a multiple of 9:
- 201: 201/9 = 22.33 (not a whole number)
- 205: 205/9 = 22.78 (not a whole number)
- 207: 207/9 = 23 (is a whole number)
- 210: 210/9 = 23.33 (not a whole number)
Hence, the possible value of (a + b + c) is 207.
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