Question

If \(\frac{1}{3}\) of A is equal to 70% of B and \(\frac{2}{3}\) of C is equal to 25% of A, then A:B:C =

• A. 80:63:44
• B. 63:44:84
• C. 40:18:15
• D. 168:80:63

Hint:

When two ratios contain a common term, first make the common term equal using LCM and then combine the ratios directly.

Answer 1

The Correct Option is D

Concept: Convert the given percentage relations into fractional ratios and then combine the ratios by making the common term equal.

Step 1: Finding the ratio between A and B.
\[ \frac{A}{3}=70\%\text{ of }B=\frac{7}{10}B \] \[ A=\frac{21}{10}B \] \[ A:B=21:10 \]

Step 2: Finding the ratio between C and A.
\[ \frac{2}{3}C=25\%\text{ of }A=\frac{1}{4}A \] \[ C=\frac{3}{8}A \] \[ C:A=3:8 \]

Step 3: Combining the ratios.
\[ A:B=21:10 \] \[ A:C=8:3 \] LCM of 21 and 8 is 168. \[ A:B=168:80 \] \[ A:C=168:63 \] Hence, \[ A:B:C=168:80:63 \] {168:80:63}