Mathematics
The sum of a two digit number and the number obtained by reversing the order of the digits is 99. Find the number, if the digits differ by 3.
Linear Equations
11 Likes
Answer
Let digit at ten's place be x and unit's place be y.
Number = 10(x) + y = 10x + y
On reversing the digits,
Reversed number = 10(y) + x = 10y + x
Given,
Sum of a two digit number and the number obtained by reversing the order of the digits is 99.
∴ (10x + y) + (10y + x) = 99
⇒ 11x + 11y = 99
⇒ 11(x + y) = 99
⇒ x + y = 9
⇒ x = 9 - y …………(1)
Given,
Digits differ by 3.
∴ x - y = 3 or y - x = 3
Considering x - y = 3
⇒ x = 3 + y ……….(2)
From (1) and (2), we get :
⇒ 9 - y = 3 + y
⇒ 9 - 3 = 2y
⇒ 2y = 6
⇒ y = 3.
Substituting value of y = 3 in equation (1), we get :
⇒ x = 9 - 3 = 6.
Number = 10x + y = 10(6) + 3 = 60 + 3 = 63.
Considering y - x = 3
⇒ x = y - 3 ……….(3)
From (1) and (3), we get :
⇒ 9 - y = y - 3
⇒ 9 + 3 = 2y
⇒ 2y = 12
⇒ y = 6.
Substituting value of y = 6 in equation (1), we get :
⇒ x = 9 - 6 = 3.
Number = 10x + y = 10(3) + 6 = 30 + 6 = 36.
Hence, number = 36 or 63.
Answered By
6 Likes
Related Questions
1250 persons went to see a circus-show. Each adult paid ₹ 75 and each child paid ₹ 25 for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to ₹ 61,250.
Rohit says to Ajay, "Give me a hundred, I shall then become twice as rich as you." Ajay replies, "if you give me ten, I shall be six times as rich as you." How much does each have originally?
Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.
From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B, the total cost is ₹ 77. But if we buy 3 tickets for station A and 5 tickets for station B, the total cost is ₹ 124. What are the fares from Delhi to station A and to station B ?