Question

If a is $\frac{3}2$ times of b, b is $\frac{3}{4}^{th}$ of c and d is $\frac{1}4 ^{th}$ of c, the ratio of a and d is

• A. 8:3
• B. 9:1
• C. 8:1
• D. 9:2

Answer 1

The Correct Option is D

To solve this problem, we need to find the ratio of \(a\) to \(d\) given the relationships between \(a\), \(b\), \(c\), and \(d\). 

1. First, express \(a\) in terms of \(b\):
   • \(a = \frac{3}{2} \times b\)
2. Next, express \(b\) in terms of \(c\):
   • \(b = \frac{3}{4} \times c\)
3. Now, express \(d\) in terms of \(c\):
   • \(d = \frac{1}{4} \times c\)
4. Now substitute the expressions for \(b\) and \(d\) back to express \(a\) in terms of \(d\):
   • Substitute \(b = \frac{3}{4} \times c\) into \(a = \frac{3}{2} \times b\):
   • \(a = \frac{3}{2} \times \left( \frac{3}{4} \times c \right) = \frac{9}{8} \times c\)
5. Now use \(d = \frac{1}{4} \times c\):
   • Express \(c\) in terms of \(d\): \(c = 4 \times d\)
   • Substituting in \(a = \frac{9}{8} \times c\), we have \(a = \frac{9}{8} \times (4 \times d)\).
   • Therefore, \(a = \frac{9}{8} \times 4 \times d = \frac{36}{8} \times d = \frac{9}{2} \times d\)
6. Finally, calculate the ratio of \(a\) to \(d\):
   • The ratio \(\frac{a}{d} = \frac{9/2 \times d}{d} = \frac{9}{2}\)
   • Therefore, the ratio of \(a\) to \(d\) is \(9:2\).

The correct option is 9:2.