If \(60\% of A = 0.3 of B = 16 of C\) , find \(A : B : C\) .

Question

If \(60\% of A = 0.3 of B = 16 of C\) , find \(A : B : C\) .

1. A. 5 : 10 : 18 (Correct answer)
2. B. 18 : 10 : 5
3. C. 6 : 3 : 10
4. D. 10 : 5 : 18

Correct Answer

Option A — 5 : 10 : 18

Detailed Solution & Explanation

The correct answer is 5 : 10 : 18.

Key Points

• Set all three equal to a common value k: 60% of A = 0.3 of B = (1/6) of C = k.
• Solve each for its variable:
  • A = k / 0.6 = 5k/3
  • B = k / 0.3 = 10k/3
  • C = 6k = 18k/3
• Putting them over the same denominator gives A : B : C = 5k/3 : 10k/3 : 18k/3 = 5 : 10 : 18.
• Note the ordering trap: option B is the same numbers reversed, and option D swaps A and B. Once you equate to k, the variable with the largest coefficient (C, at 1/6) must be the largest term.
• Whenever several percentages of different quantities are equal, set them to k and solve individually — never compare the percentages directly.

Additional Information

• When several different percentages of different quantities are declared equal, setting them all to a common k is the general method — it works for any number of terms.
• Percentages convert to fractions that make ratios instant: 60% = 3/5, 0.3 = 3/10, 1/6 stays as it is.
• A ratio can be scaled by any constant, so always clear denominators at the end (multiply through by 3 here) to reach the whole-number form the options use.

प्रश्न (हिन्दी में)

यदि \(A का 60\% = B का 0.3 = C का 16\) है, तो \(A : B : C\) ज्ञात कीजिए।

1. A. 5 : 10 : 18
2. B. 18 : 10 : 5
3. C. 6 : 3 : 10
4. D. 10 : 5 : 18