A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.
Answers
Given : A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places.
Solution:
Let the digit in the unit's place be x and the digit at the tens place be y.
Number = 10y + x
The number obtained by reversing the order of the digits is = 10x + y
ATQ :
Condition : 1
xy = 20……………(1)
Condition : 2
(10y + x) + 9 = 10x + y
10x + y - 10y - x = 9
9x - 9y = 9
9(x – y) = 9
x - y = 9/9
x - y = 1
x = 1 + y …………..(2)
On Substituting the value of x in equation (1) we obtain :
(1 + y) + y = 20
y + y2 = 20
y2 + y - 20 = 0
y2 + 5y - 4y – 20 = 0
[By middle term splitting]
y(y + 5)- 4(y + 5) = 0
(y + 5)(y - 4) = 0
y = - 5 or y = 4
On putting y = - 5in eq (2) we obtain :
x = 1 + y
x = 1 + (- 5)
x =1 - 5
x = - 4
On putting y = 4 in eq (1) we obtain :
x = 1 + y
x = 1 + 4
x = 5
x = - 4 and y = - 5 pair of solution are both negative. So, we cant take this pair.
From x = 5 and y = 4 we obtain a number :
Number = 10y + x = 10 × 4 +5 = 40 + 5 = 45
Hence, the number is 45.
Hope this answer will help you…
Some more questions from this chapter :
A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
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A two-digit number is 4 times the sum of its digits and twice the product of the digits.Find the number.
https://brainly.in/question/17190153
Step-by-step explanation:
The desired number is 45
