question_answer 22)

                One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

Answer:

                Let in the original number Case I. Units digit \[=x\] Then, tens digit \[=3x\] Original number \[=(3x)\times 10+x\] \[=30x+x\] \[=31x\] On interchanging the digits Units digit \[=3x\] and, tens digit \[=x\] \[\therefore \] Resulting number \[=x+10+3x\] \[=10x+3x\] \[=13x\] According to the question, \[13x+31x=88\] \[\Rightarrow \]               \[44x=88\] \[\Rightarrow \]               \[x=\frac{88}{44}=2\]                     | Dividing both sides by 44 \[\Rightarrow \]               \[3x=3\times 2=6\] Hence, the original number is 62. Check:   \[6=3\times 2\] \[62+26=88\] Hence, the result is verified. Case II. Tens digit \[=x\] Then, units digit \[=3x\] \[\therefore \] Original number \[=x\times 10+3x\] \[=10x+3x\] \[=13x\] Units digit \[=x\] and        tens digit \[=3x\] \[\therefore \] Resulting number \[=(3x)\times 10\times x\] \[=30x+x\] \[=31x\]                 According to the question, \[31x+13x=88\] \[\Rightarrow \]               \[44x=88\] \[\Rightarrow \]               \[x=\frac{88}{44}=2\]                     | Dividing both sides by 44 \[\Rightarrow \]               \[3x=6\] Hence, the original number is 26 Check:  \[6=3\times 2\] \[26+62=88\] Hence, the result is verified.