a two digit number is 4 times the sum of its digits.The sum of the number formed by reversing its digits and 9 is equal to 2 times the orginal number.Find the number
Answers
Answer:-
Let the digit at one's place be y and ten's place be x.
The number will be 10x + y.
Given:
The number is 4 times the sum of the digits.
→ 10x + y = 4 (x + y)
→ 10x + y = 4x + 4y
→ 10x - 4x = 4y - y
→ 6x = 3y
→ x = 3y/6
→ x = y/2 -- equation (1)
And,
Sum of the number formed by reversing the digits and 9 = Twice the original number.
→ (10y + x) + 9 = 2 (10x + y)
→ 10y + x + 9 = 20x + 2y
→ 10y - 2y + x - 20x = - 9
→ 8y - 19x = - 9
Putting the value of x from equation (1) we get,
→ 8y - 19 (y/2) = - 9
→ (16y - 19y) / 2 = - 9
→ - 3y = - 9 * 2
→ y = - 9 * 2 / - 3
→ y = 6
Putting the value of y in equation (1) we get,
→ x = y/2
→ x = 6/2
→ x = 3
→ The number = 10 * 3 + 6 = 30 + 6 = 36.
Hence, the required number is 36.
Verification:-
The number is 4 times the sum of its digits.
→ 36 = 4 (3 + 6)
→ 36 = 4 * 9
→ 36 = 36.
Sum of the number formed by reversing the digits and 9 = twice the original number.
→ 63 + 9 = 2 * 36
→ 72 = 72
Hence, Verified.
Answer:
⭐ Question ⭐
✏ A two digit number is 4 times the sum of its digits.The sum of the number formed by reversing its digits and 9 is equal to 2 times the orginal number.Find the number.
⭐ Solution ⭐
✏Let the digit at one's place be y
✏ And ten's be x
➡ Given:-
✍ The number is 4 times the sums of the digits.
=> 10x+y = 4(x+y)
=> 10x+y = 4x+4y
=> 10x-4x = 4y-y
=> 6x = 3y
=> x = 3y/6
=> x = y/2 --------(1)
And,
✍ Sum of the number form by the reserving the digits and 9 = Twice the original number.
=> (10y+x)+9 = 2(10x+y)
=> 10y+x+9 = 20x+2y
=> 10y-2y+x-20x = -9
=> 8x-19x = -9
➡ Putting the value of x in the equation (1) we get,
=> 8y-19(y/2) = -9
=> (16y-19y)/2 = -9
=> -3y = -9×2/-3
=> y = 6
➡ Putting the value of y in the equation (1) we get,
=> x = y/2
=> x = 6/2
=> x = 3
✏ The number is =10×3+6=30+6=36✔
Step-by-step explanation: