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.

Number of the number of Digital watches sold by C is what percentage of analog watches sold by A and C together.

The correct option is 70%.

Let us analyze the given information step-by-step to find the values for each shop:

Step 1: Find the watches sold by Shop B
The number of analog watches sold by B is given as 30, which is 25% less than the digital watches sold by him.
Let the number of digital watches sold by B be $B_{\text{digital}}$.
Since $B_{\text{analog}}=30$, we have:
$30=B_{\text{digital}}\times (1-0.25)$
$30=0.75\times B_{\text{digital}}$
$B_{\text{digital}}=\frac{30}{0.75}=40$
So, Shop B sold 30 analog watches and 40 digital watches.

Step 2: Find the watches sold by Shop A
The ratio of analog watches sold by A to digital watches sold by B is 5:4.
$A_{\text{analog}}=\frac{5}{4}\times B_{\text{digital}}$
$A_{\text{analog}}=\frac{5}{4}\times 40=50$
The number of digital watches sold by A is 25% less than that of B.
$A_{\text{digital}}=40\times (1-0.25)=40\times 0.75=30$
So, Shop A sold 50 analog watches and 30 digital watches.

Step 3: Find the watches sold by Shop C
The total number of digital watches sold by all three shops is 140.
$A_{\text{digital}}+B_{\text{digital}}+C_{\text{digital}}=140$
$30+40+C_{\text{digital}}=140$
$C_{\text{digital}}=140-70=70$
The number of digital watches sold by C is 40% more than the analog watches sold by C.
$C_{\text{digital}}=1.40\times C_{\text{analog}}$
$70=1.40\times C_{\text{analog}}$
$C_{\text{analog}}=\frac{70}{1.4}=50$
So, Shop C sold 50 analog watches and 70 digital watches.

Step 4: Calculate the required percentage
We need to find what percentage the digital watches sold by C ($C_{\text{digital}}$) is of the analog watches sold by A and C together ($A_{\text{analog}}+C_{\text{analog}}$).
Total analog watches sold by A and C together:
$A_{\text{analog}}+C_{\text{analog}}=50+50=100$
Required Percentage:
$\text{Percentage}=\frac{C_{\text{digital}}}{A_{\text{analog}}+C_{\text{analog}}}\times 100$
$\text{Percentage}=\frac{70}{100}\times 100=70\%$