Maths · Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
A two-digit number is 3 more than six times the sum of its digits. If 18 is adde
A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number
- A. 25
- B. 45
- C. 75
- D. None of these
Step-by-step solution
Let the tens digit be x and the units digit be y. Then the number is 10x+y. From the first condition: 10x+y = 6(x+y)+3, which simplifies to 4x-5y=3. From the second condition: 10y+x+18=10x+y, which simplifies to y-x+2=0 or y=x-2. Substituting gives 4x-5(x-2)=3 → -x+10=3 → x=7, then y=5. Thus the number is 75.
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