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.

First, let's analyze the given data step-by-step to find the number of watches sold by each shop.

Step 1: Calculate the number of watches sold by Shop B
We are given that the number of analog watches sold by B ($B_{\text{analog}}$) is 30, which is 25% less than the number of digital watches sold by B ($B_{\text{digital}}$).
Therefore, we can set up the following equation:
$B_{\text{analog}}=B_{\text{digital}}\times (1-0.25)$
$30=0.75\times B_{\text{digital}}$
$B_{\text{digital}}=\frac{30}{0.75}=40$
So, the number of digital watches sold by B is 40, and the number of analog watches sold by B is 30.

Step 2: Calculate the number of watches sold by Shop A
The ratio of the number of analog watches sold by A ($A_{\text{analog}}$) to the number of digital watches sold by B ($B_{\text{digital}}$) is 5 : 4.
$\frac{A_{\text{analog}}}{B_{\text{digital}}}=\frac{5}{4}$
Substituting the value of $B_{\text{digital}}=40$:
$A_{\text{analog}}=\frac{5}{4}\times 40=50$
The number of digital watches sold by A ($A_{\text{digital}}$) is 25% less than that of B:
$A_{\text{digital}}=40\times (1-0.25)=30$

Step 3: Calculate the number of digital watches sold by Shop C
The total number of digital watches sold by all three shops is 140.
$A_{\text{digital}}+B_{\text{digital}}+C_{\text{digital}}=140$
Substituting the known values:
$30+40+C_{\text{digital}}=140$
$70+C_{\text{digital}}=140$
$C_{\text{digital}}=140-70=70$

Step 4: Find the required ratio
We need to find the ratio of the number of analog watches sold by B to the number of digital watches sold by C.
Number of analog watches sold by B = 30
Number of digital watches sold by C = 70
The required ratio is:
$\text{Ratio}=30:70=3:7$