A shopkeeper sold a certain number (a two-digit number) of toys all priced at a certain value (also a two-digit number when expressed in rupees). By mistake he reversed the digits of both, the number of items sold and the price of each item. In doing so, he found that his stock left at the end of the day showed 72 items more than what it actually was.

1. What could be the actual number of toys sold?
A) 19 B) 49 C) 91 D) 94

2. If the faulty calculations show a total sale of rs1577, what was the actual selling price of each toy?
A) rs 38 B) rs 57 C) rs 75 D) rs 83

Question

A shopkeeper sold a certain number (a two-digit number) of toys all priced at a certain value (also a two-digit number when expressed in rupees). By mistake he reversed the digits of both, the number of items sold and the price of each item. In doing so, he found that his stock left at the end of the day showed 72 items more than what it actually was.

1. What could be the actual number of toys sold?
A) 19   B) 49   C) 91   D) 94

2. If the faulty calculations show a total sale of rs1577, what was the actual selling price of each toy?
A) rs 38   B) rs 57   C) rs 75   D) rs 83

anonymous · Answer

okay so this is how i figured out the answer if anybody attempts this in the future.

the number of items sold (2digit number) and the number you get by reversing its digits are given as:

10y - x - (10x - y) = 72
9y - 9x =72
y - x = 8 .... (1)

for (1) what values of (y - x) = 8? the possible values are 9 - 1 = 8. or 8 - 0 which imo is not possible because the reversal of its digits (let's say the original number wouldn't be a one digit number.)
therefore,  91 items were sold that day.

as for the second part of the question, since the wrongly recorded number of items sold was 19. divide 1577 (total sales) by 19 to get rs 83 (the wrongly recorded price of a toy). reverse this amount to get the correct amount i.e rs 38.