Question

ans this q urgent 5 and 7th q

Answer 1

5) Solution :
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Given :
Statement 1 : The sum of a number and the number obtained by reversing it's digits  is 66.

Let the digits be x and y,.  (xy)
In expanded form : 10x + y,.
When the digits are reversed,.
It changes into : 10y + x,.
Sum of the number and number obtained by reversing it's digits = 66

⇒ 10x + y + 10y + x = 66

⇒ 11x + 11y = 66
⇒ 11(x + y) = 11(6)
⇒ x + y = 6 ...(i)
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Statement 2 :

The difference between the two digits = 2 Then,
Either,  x - y = 2 (or) y - x = 2 ..(ii)

By solving,.
By adding both the equations,. 
⇒ (x + y) + (x - y) = 6 + 2

⇒ 2x = 8
⇒ x = 4,.
By substituting the value of x in equation (ii),

We get,.
⇒ x - y = 2

⇒ 4 - y = 2

⇒ - y = 2 - 4
⇒ - y = - 2 
⇒ y = 2,.
Hence, the number is 24,.
if y - x = 2,.
Then,.
By solving,.

The number would be 42,.
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7) Solution :
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Given :
Statement 1 : The sum of a number and the number obtained by reversing it's digits  is 99.

Let the digits be x and y,.  (xy)
In expanded form : 10x + y,.
When the digits are reversed,.
It changes into : 10y + x,.
Sum of the number and number obtained by reversing it's digits = 66

⇒ 10x + y + 10y + x = 66

⇒ 11x + 11y = 99

⇒ 11(x + y) = 11(9)
⇒ x + y = 9 ...(i)
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Statement 2 :
The 2 digits differ by 3,.
Then,
Either,  x - y = 3 (or) y - x = 3
By Adding (i) & (ii)
We get,
⇒ (x + y) + (x - y) = 9 + 3
⇒ 2x = 12
⇒ x = 6,.
By substituting the value of x in equation (ii),
We get,.
⇒ 6 - y = 3
⇒ -y = 3 - 6
⇒ -y = -3
⇒ y = 3,.
Hence, the number is 63,.
if y - x = 3,.
Then,.
By solving,.

The number would be 36,.