ICSE Class X Math 2014 Solved Paper
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Question : 44
Total: 52
A two digit positive number is such that the product of its digits is 6 . If 9 is added to the number, the digits interchange their places. Find the number.
Solution:
Let the required two digit number be 10 x + y
Given :x y = 6 10 x + y + 9 = 10 y + x
10 x − x + y − 10 y + 9 = 0
⇒ 9 x − 9 y + 9 = 0
⇒ x − y + 1 = 0
⇒ y = x + 1
x y = 6 (given)
⇒ x ( x + 1 ) = 6
⇒ x 2 + x − 6 = 0
⇒ x 2 + 3 x − 2 x − 6 = 0
⇒ ( x + 3 ) ( x − 2 ) = 0
⇒ x = − 3 , 2
Rejecting x = − 3
When x = 2 , y = x + 1 = 2 + 1 = 3
∴
= 10 x + y
= 10 × 2 + 3 = 23
Given :
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