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A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold?
a)27
b)91
c)83
d)None of these?
a)27
b)91
c)83
d)None of these?
Most Upvoted Answer
A shopkeeper uses a “point of sales” software which prepares the bill ...
Problem Analysis:
Let's assume the quantity of units is represented by XY (where X is the tens digit and Y is the units digit) and the price is represented by AB (where A is the tens digit and B is the units digit). According to the problem, the shopkeeper swaps the digits of both the quantity of units and the price. So, the actual quantity of units is represented by YX and the actual price is represented by BA.
Given Information:
Closing stock balance is lowered by 72 units, which means the actual quantity of units is higher than the quantity shown on the bill by 72 units. The sales value shown on the bill is Rs 1,368.
Calculating the Actual Quantity of Units:
Let's assume the quantity shown on the bill is Q units. Since the actual quantity of units is higher by 72 units, we can write the equation:
Actual Quantity of Units = Quantity shown on the bill + 72
YX = XY + 72
10Y + X = 10X + Y + 72
9Y - 9X = 72
Y - X = 8
Calculating the Actual Price:
Since the shopkeeper swaps the digits of the price, the actual price becomes BA. We can write the equation:
Actual Price = Price shown on the bill
BA = AB
10B + A = 10A + B
9B - 9A = 0
B - A = 0
Calculating the Sales Value:
The sales value shown on the bill is Rs 1,368, which is equal to the quantity shown on the bill multiplied by the price shown on the bill.
Sales Value = Quantity shown on the bill * Price shown on the bill
XY * AB = 1368
(10X + Y) * (10A + B) = 1368
100AX + 10AY + BX + BY = 1368
100AX + 10AY + AX + AY = 1368
101AX + 11AY = 1368
101AX + 11(8 + X) = 1368
101AX + 88 + 11X = 1368
112AX + 11X = 1368 - 88
123AX + 11X = 1280
11X(11A + 1) = 1280
Calculating the Possible Values of X and A:
To find the possible values of X and A, we need to find the factors of 1280 that satisfy the equation 11X(11A + 1) = 1280.
The factors of 1280 are: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, and 1280.
We need to check which of these factors satisfy the equation 11X(11A + 1) = 1280.
Possible Values of X and A:
- X = 16 and A = 10
- X = 32 and A = 5
- X = 64 and A = 2
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Let's assume the quantity of units is represented by XY (where X is the tens digit and Y is the units digit) and the price is represented by AB (where A is the tens digit and B is the units digit). According to the problem, the shopkeeper swaps the digits of both the quantity of units and the price. So, the actual quantity of units is represented by YX and the actual price is represented by BA.
Given Information:
Closing stock balance is lowered by 72 units, which means the actual quantity of units is higher than the quantity shown on the bill by 72 units. The sales value shown on the bill is Rs 1,368.
Calculating the Actual Quantity of Units:
Let's assume the quantity shown on the bill is Q units. Since the actual quantity of units is higher by 72 units, we can write the equation:
Actual Quantity of Units = Quantity shown on the bill + 72
YX = XY + 72
10Y + X = 10X + Y + 72
9Y - 9X = 72
Y - X = 8
Calculating the Actual Price:
Since the shopkeeper swaps the digits of the price, the actual price becomes BA. We can write the equation:
Actual Price = Price shown on the bill
BA = AB
10B + A = 10A + B
9B - 9A = 0
B - A = 0
Calculating the Sales Value:
The sales value shown on the bill is Rs 1,368, which is equal to the quantity shown on the bill multiplied by the price shown on the bill.
Sales Value = Quantity shown on the bill * Price shown on the bill
XY * AB = 1368
(10X + Y) * (10A + B) = 1368
100AX + 10AY + BX + BY = 1368
100AX + 10AY + AX + AY = 1368
101AX + 11AY = 1368
101AX + 11(8 + X) = 1368
101AX + 88 + 11X = 1368
112AX + 11X = 1368 - 88
123AX + 11X = 1280
11X(11A + 1) = 1280
Calculating the Possible Values of X and A:
To find the possible values of X and A, we need to find the factors of 1280 that satisfy the equation 11X(11A + 1) = 1280.
The factors of 1280 are: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, and 1280.
We need to check which of these factors satisfy the equation 11X(11A + 1) = 1280.
Possible Values of X and A:
- X = 16 and A = 10
- X = 32 and A = 5
- X = 64 and A = 2
-
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A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these?
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A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these?.
A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper uses a “point of sales” software which prepares the bill for customers based on the number of units per unit. Both of the above are 2-digit numbers. While entering the data, he erroneously swaps the digits of both quantity of units and price. As a result, the closing stock balance is lowered by 72 units, and the sales value shown is Rs 1,368. How many units have actually been sold? a)27 b)91 c)83 d)None of these?.
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