The sum of digits of a two-digit number is 7. If the digits are reversed and the resulting number is decreased by 2, twice of the original number is obtained. Find the original numberClass: 10

# The sum of digits of a two-digit number is 7. If the digits are reversed and the resulting number is decreased by 2, twice of the original number is obtained. Find the original numberClass: 10

1. A
27
2. B
29
3. C
25
4. D
20

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### Solution:

Let the unit place = x of the number
Let the tenth place of the number = y
Number = 10y + x
x + y = 7   ________(i)
Reversed number = 10x + y
According to question
(10x + y) 2 = 2(10y + x)
10x + y 2 = 20y + 2x
8x 19y = 2  _______(ii)
From eqn (i) & eqn (ii)
x + y = 7 19
8x 19y = 2
27x = 135
n = 5
Put in eqn (i)
x + y = 7
5 + y = 7
y = 2
Number = 10y + x
= 10 2 + 5 = 25

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