A cashier accidentally typed a two-digit price in reverse order on a receipt. The customer was charged based on the incorrect number. Interestingly, the product of the actual price and the mistyped price turned out to be ₹1944. What is the difference between the actual and mistyped prices?
(a) 40
(b) 48
(c) 60
(d) 45

Question

A cashier accidentally typed a two-digit price in reverse order on a receipt. The customer was charged based on the incorrect number. Interestingly, the product of the actual price and the mistyped price turned out to be ₹1944. What is the difference between the actual and mistyped prices?
(a) 40
(b) 48
(c) 60
(d) 45

ONLiNE UPSC · Accepted Answer

Let the actual price be a two-digit number p, and its mistyped version be q, which is just the reversal of digits of p.
We are told:
p &times; q = 1944
Let&rsquo;s express the number p = 10a + b
Then the reversed number is:
q = 10b + a
Now multiply:
(10a + b) * (10b + a) = 1944
(10a + b) * (10b + a) = (10a)(10b)+(10a)(a)+b(10b)+b(a) = 100ab + 10a2 + 10b2 + ab = 101ab + 10a2 + 10b2 = 1944
On solving. We get
p = 72 then q = 27:
72 &times; 27 = 1944
Thus, actual and mistyped prices are 72 and 27.
Their difference is:
|72 &minus; 27| = 45

Hence, option d is correct.

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M Question 1	⏱ 0
A cashier accidentally typed a two-digit price in reverse order on a receipt. The customer was charged based on the incorrect number. Interestingly, the product of the actual price and the mistyped price turned out to be ₹1944. What is the difference between the actual and mistyped prices? (a) 40 (b) 48 (c) 60 (d) 45