Direction (63-65): Read the information carefully and answer the following questions.

Three shops (A, B and C) sold two types of watches (Analog and Digital). Ratio of number of Analog watches sold by shop A to the number of digital watches sold by B is 5: 4 and the number of Digital watches sold by A is 25% less than that of B. Number of digital watches sold by C is 40% more than that of analog by C. Number of analog watches sold by B is 30 which 25% less than that of digital watches sold by him and the total number digital watches sold by all the three shops is 140.

Find the ratio of the number of Analog watches sold by B to the number of Digital watches sold by C.

Let us break down the given information step-by-step to find the required ratio.

First, let us analyze the data given for shop B:
The number of analog watches sold by B is 30.
This number (30) is 25% less than the number of digital watches sold by B.
Let the number of digital watches sold by B be $D‎B_{}$.
Since the analog watches sold by B (30) is 25% less than $D‎B_{}$, we have:
$30=(1-0.25)\times D‎B_{}$
$30=0.75\times D‎B_{}$
$D‎B_{}=\frac{30}{0.75}=40$.
So, the number of digital watches sold by B is 40.

Next, let us find the details for shop A:
The ratio of the number of analog watches sold by shop A ($A‎A_{}$) to the number of digital watches sold by B ($D‎B_{}=40$) is 5:4.
Therefore:
$\frac{A‎A_{}}{40}=\frac{5}{4}$
$A‎A_{}=40\times \frac{5}{4}=50$.
So, shop A sold 50 analog watches.
The number of digital watches sold by A ($D‎A_{}$) is 25% less than that of B ($D‎B_{}=40$):
$D‎A_{}=40\times (1-0.25)=40\times 0.75=30$.
So, shop A sold 30 digital watches.

Now, let us find the details for shop C:
We are given that the total number of digital watches sold by all three shops is 140.
$D‎A_{}+D‎B_{}+D‎C_{}=140$
Substituting the known values:
$30+40+D‎C_{}=140$
$70+D‎C_{}=140$
$D‎C_{}=140-70=70$.
So, the number of digital watches sold by shop C is 70.

Finally, we need to find the ratio of the number of analog watches sold by B to the number of digital watches sold by C:
The number of analog watches sold by B is 30.
The number of digital watches sold by C is 70.
The required ratio is:
$\text{Ratio}=\frac{30}{70}=\frac{3}{7}$
This can be written as 3:7.