plzz solve this two question
1. The units digit of a two-digit number is 3 and seven times the sum of the digits is the
number itself. Find the number.
2. In a two-digit number, the digit at the units place is double the digit in the tens place. The number
exceeds the sum of its digits by 18. Find the number.
A wo digit number is 3 more than 4 times the sum of its digits If is is added to the
Answers
Answer 1.
Number = 63
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Explanation
Let ten's digit be x and unit digit be y.
Number = 10x + y
According to question
The units digit of a two-digit number is 3
⇒ y = 3 ___ (eq 1)
Seven times the sum of the digits is the
number itself.
⇒ 7(x + y) = 10x + 3
⇒ 7x + 7(3) = 10x + 3 [From (eq 1)]
⇒ 7x - 21 = 10x + 3
⇒ 10x - 7x = - 3 + 21
⇒ 3x = 18
⇒ x = 6
•°• Number = 10x + y
⇒ 10(6) + 3
⇒ 60 + 3
⇒ 63
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Answer 2.
Number = 24
_____________________
Explanation
Let ten's digit number be x and unit digit number be y.
Number = 10x + y
According to question
The digit at the units place is double the digit in the tens place.
⇒ y = 2x ___ (eq 1)
The number exceeds the sum of its digits by 18.
⇒ 10x + y = x + y + 18
⇒ 10x - x + y - y = 18
⇒ 9x = 18
⇒ x = 2
Put value of x in (eq 1)
⇒ y = 2(2)
⇒ y = 4
Number = 10x + y
⇒ 10(2) + 4
⇒ 24
Number = 63
Given :
- The units digit of a two-digit number is 3
- Seven time the sum of the digits is the number itself.
To find :
- The Number.
Solution :
Let the digit in the tens place be x.
The units digit = 3. [Given]
Original number = 10x + 3
- Seven time the sum of the digits is the number itself.
Constituting it mathematically,
______________________________
Number = 24
Given :
- In a two-digit number, the digit at the units place is double the digit in the tens place.
- The number exceeds the sum of its digits by 18.
To find :
- The number.
Solution :
Let the digit in the tens place be x.
Let the digit in the units place be y.
Original number = 10x + y
- The digit at the units place is double the digit in the tens place.
Constituting it mathematically,
---> (1)
- The number exceeds the sum of its digits by 18.
Constituting it mathematically,
Substitute x = 2 in equation 1,
y = 2x
y = 2(2)
y = 4