Example 10 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Important Question)
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Example 10
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
Number is of the form
Let Digit at Units place = y
& Digit at Tens place = x
Given that
(Number) + (Reversed Number) = 66
(10x + y) + (10y + x) = 66
10x + x + 10y + y = 66
11x + 11y = 66
x + y = 66/11
x + y = 6
Also, given that
Digits of the number differ by 2,
So x – y = 2
or
y – x = 2
Solving equation (1) & (2)
x + y = 6 …(1)
x – y = 2 …(2)
By elimination method
2y = 4
y = 4/2
y = 2
Putting y = 2 in (2)
x – y = 2
x – 2 = 2
x = 4
Hence, x = 4, y = 2 is the solution of equations (1) & (2)
Thus,
Number is = 10x + y
= 10 (4) + 2
= 40 + 2
= 42
Solving equation (1) & (3)
x + y = 6 …(1)
y – x = 2 …(3)
Solving (1) & (3) by elimination
2x = 4
x = 4/2
x = 2
Putting x = 2 in equation (3)
y – x = 2
y – 2 = 2
y = 2 + 2
y = 4
Hence x = 2, y = 4 is the solution of equations (1) & (2)
Thus,
Number is = 10x + y
= 10 (2) + 4 = 20 + 4
= 24
So, the numbers which satisfy the given equations are 24 & 42
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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