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.

Total number of Analog watches sold by all the three shop is how much more/less than the number of Digital watches sold by A and B together.

The correct answer is 60.

Step-by-step Derivation:

Let the number of analog and digital watches sold by shops A, B, and C be represented by $A_{\text{Analog}}$, $A_{\text{Digital}}$, $B_{\text{Analog}}$, $B_{\text{Digital}}$, $C_{\text{Analog}}$, and $C_{\text{Digital}}$ respectively.

Step 1: Find the number of watches sold by Shop B
We are given that the number of analog watches sold by shop B is 30, which is 25% less than the number of digital watches sold by shop B.
Thus, we can write:
$B_{\text{Analog}}=30$
$B_{\text{Analog}}=(1-0.25)\times B_{\text{Digital}}$
$30=0.75\times B_{\text{Digital}}$
$B_{\text{Digital}}=\frac{30}{0.75}=40$

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

Step 3: Find the number of watches sold by Shop C
We are given that 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:
$30+40+C_{\text{Digital}}=140$
$70+C_{\text{Digital}}=140$
$C_{\text{Digital}}=70$
We are also given that the number of digital watches sold by C is 40% more than the number of analog watches sold by C:
$C_{\text{Digital}}=1.4\times C_{\text{Analog}}$
$70=1.4\times C_{\text{Analog}}$
$C_{\text{Analog}}=\frac{70}{1.4}=50$

Step 4: Answer the final question
First, calculate the total number of analog watches sold by all three shops:
${\text{Total Analog}}_{}=A_{\text{Analog}}+B_{\text{Analog}}+C_{\text{Analog}}$
${\text{Total Analog}}_{}=50+30+50=130$
Next, calculate the total number of digital watches sold by shops A and B together:
${\text{Digital}}_{A+B}=A_{\text{Digital}}+B_{\text{Digital}}$
${\text{Digital}}_{A+B}=30+40=70$
Now, find the difference to determine how much more the total number of analog watches is compared to the digital watches sold by A and B together:
$\text{Difference}=130-70=60$