Choose the correct answer.
If we multiply a two-digit number by the sum of its digits, we get 648. If we reverse the order
of digits of the number and multiply it by the sum of digits, we get 243.
Find the number.
А
81
B
72
C
18
D 27
Answers
Answer:
72
Step-by-step explanation:
let sum of the digits be S and 2digits of no. be x,y
x+y=s
10x+y × s=648 --A
10y+x × s =243 ---B
A-B
9(x-y)(x+y) =405
(x-y)(x+y) = 45
A+B
11(x+y)^2 = 891
(x+y)^2= 81
x+y =9
x-y =5
=>x=7, y=2
so no. is 72
hope this helps
The number is 72.
Given: Multiplying a 2-digit number by the sum of digits gives 648.
Multiplying the reverse of the 2-digit number by the sum of digits gives 243.
To Find: The number
Solution: Let the number be 10x + y.
Let, the sum of digits be x + y
Now, multiplying the 2-digit number by the sum of digits gives 648.
(10x + y) * (x + y) = 648 (Equation 1)
Similarly multiplying the reverse of the 2-digit number by the sum of digits gives 243.
(10y + x) * (x + y) = 243 (Equation 2)
Dividing equation 1 by 2 we get,
By performing cross multiplication we get,
30x + 3y = 80y + 8x
22x - 77y = 0
2x - 7y = 0
Since, 7 and 2 are the roots of the above equation, put x = 7 and y = 2
(2 * 7) - (7 * 2) = 0
Now, putting x = 7 and y = 2 in the 2-digit number:
10 * 7 + 2 = 72
Therefore, the number is 72.
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