Question

If the digit 1 is placed after a two-digit number whose ten’s digit is l and unit’s digit is u, then the new number would be equal to
(A). $10l+u+1$
(B). $100l+10u+1$
(C). $1000l+10u+1$
(D). $l+u+1$

Answer 1

Hint: In this case, digit 1 is being placed after the two-digit number, therefore the new unit’s place number would be 1, and l and u would occupy the hundred’s and tens place in the new number. Then using the formula for the value of the number in terms of its place value and face value we can find the expression for the new number to obtain the answer to this question.

Complete step-by-step solution -
We are given that in the old number, the ten’s digit is l and unit’s digit is u, therefore it is of the form lu.
Now, when 1 is placed after this number, the number would be of the form lu1.
Therefore, in the new number, the place value of l would be 100, the place value of u would be 10 and the place value of 1 would be 1………………………….(1.1)
As we know that the expression for the value of a number can be written as
Value of the number= $\sum{{}}$digit$\times $ place value of the digit ……………………..(1.2)
Therefore, as the new number is of the form lu1, using (1.1) and (1.2), its value would be given by
Value of the new number = l$\times $100+u$\times $10+1$\times $1= 100l+10u+1
Which matches option (b). Hence, option (b) is the correct answer to this question.

Note: We should note that it is given that 1 is placed after the two-digit number, therefore the place value of not only 1 but also all the digits will be changed because the units digit will move to the tens place, tens digit will move to the hundreds place and so on.