Answer:

Let the units digit of the two-digit number be y and the tens digit be x.

Hence, the number will be 10x+y.

Given that the sum of digits is 12.

Hence, x+y=12.......(i)

It is also given that the new number formed by reversing the digits is greater than the original number by 54.

On reversing the digits, x becomes the units digit and y becomes the tens digit.

Hence, the new number will be 10y+x.

∴ 10y+x=10x+y+54

⇒9y−9x=54

⇒y−x=6

⇒−x+y=6.........(ii)

Adding (i) and (ii), we get:

(x+y)+(−x+y)=12+6

⇒2y=18

∴ y=

2

18

=9

Substituting y=9 in (i), we get:

x+9=12

∴ x=12−9=3

The units digit is 3 and the tens digit is 9.

Hence, the number is 39.

Checking the solution:

Original number =39

Hence, number obtained by reversing the digits =93

93=39+54

Hence, the number obtained by reversing the digits is greater than the original number by 54.

Step-by-step explanation:

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Exponents and Powers Class 8 Notes for chapter 12 given here are a great study tool to boost productivity and improve overall knowledge about the topics. In 8th standard, the concept of exponents, powers and their applications in the real world are explained clearly. This chapter help students to build a strong foundation on the concept of exponents and powers. Solved and example problems are given here for better understanding. Students can use these notes to have a thorough revision of the entire chapter and at the same be well equipped to write the exam.

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