CAT 1996 Question Paper Question 24


Answer the questions based on the following information. A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged.Although, the total sales value remained the same, i.e. Rs. 1,148, the total inventory sold got reduced by 54.

Question 24

What is the actual price per piece?


Total sales value $$= 1148 = 4\cdot7\cdot41$$
Let AB be the actual price of the product and CD be the actual quantity.

Since the quantity sold reduced by 54 upon reversing
$$CD-DC\ =\ (10\cdot C+D)-\left(10\cdot D+C\right)=9\cdot\left(C-D\right)$$
wkt, $$9\cdot\left(C-D\right)=54\ \ \longrightarrow\ \ C-D=6$$

Now, wkt, $$AB\cdot CD=1148\ \ \&\ \ BA\cdot DC=1148$$
The possible values of CD are $$93$$, $$82$$, & $$71$$
Since only 82 divides 1148, $$CD=82$$, Therefore, $$AB=14$$
Actual price and Actual quantity are 14 and 82 respectively.

Since final value $$= 1148 = 4\cdot7\cdot41$$ remains the same,
1148 can be represented as product of interchangeable numbers i.e. $$41 \times 28$$ and $$82 \times 14$$
As inventory sold reduced by 54, so, the entry of quantity sold should be 28 and price entry will be 41, and hence, actual price has to be 14 and actual sales volume has to be 82.

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