IfA : B =2: 3, B : C = 5: 7 and C : D = 3:10, then what is A:Dequal to?

Options

A. `1: 7`
B. `2:7`
C. `1 :5`
D. `5 :1`

Answer

To solve the problem of finding the ratio A:D given the ratios A:B, B:C, and C:D, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the given ratios:**
- A:B = 2:3
- B:C = 5:7
- C:D = 3:10

2. **Express the ratios in fractional form:**
- A/B = 2/3
- B/C = 5/7
- C/D = 3/10

3. **To find A:D, we can use the property of compound ratios:**
- A:D can be calculated using the formula:
\[ A:D = \frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} \]

4. **Substituting the values:**
- Substitute the values of A/B, B/C, and C/D into the formula:
\[ A:D = \left(\frac{2}{3}\right) \times \left(\frac{5}{7}\right) \times \left(\frac{3}{10}\right) \]

5. **Multiply the fractions:**
- Multiply the numerators and the denominators:
\[ A:D = \frac{2 \times 5 \times 3}{3 \times 7 \times 10} \]

6. **Simplify the expression:**
- The 3 in the numerator and denominator cancels out:
\[ A:D = \frac{2 \times 5}{7 \times 10} = \frac{10}{70} \]

7. **Further simplify the fraction:**
- Simplifying \(\frac{10}{70}\):
\[ A:D = \frac{1}{7} \]

8. **Final result:**
- Therefore, the ratio A:D is:
\[ A:D = 1:7 \]