Question

Write the quotient when the sum of two digit number 79 and the number obtained on reversing the digit is divided by
(a) 11
(b)sum of digits

Answer 1

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Write the quotient, when the sum of a 2-digit number 23 and number obtained by reversing the digits divided by

(i) 11

(ii) Sum of the digits.

Answer

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Hint: To solve the question, at first we have to expand the two digit number 23 in the form10x+y

. By obtaining the values of x and y we have to find out 10y+x

which is the number obtained by reversing the digits of the number 23. Then we will find out the sum 23 and the reversed number10y+x

. Finally we must divide the obtained sum by 11 and then by the value of the sum of the digits of 23 that is the value of x+y

to get the answers.

Complete step-by-step answer:

The given number is 23 and can be expanded in the form of 10x+y

as follows.

23=10×2+3

Here we get by comparing 10x+y

that x=3

andy=2

. Then the number obtained by reversing the digits of the number 23 is given by10y+x=10×3+2=32

.

The sum of 23 and the reversed number 32 is given by

23+32=55

When we divide 55 by 11, we know that 55 is product of factor of prime numbers 5 and 11 so, we can write 55 as 5×11, that means5511=5×1111

On solving, we get 5 as quotient that is 5×1111=5

The sum of digits of 23 is given by

x+y=2+3=5

.

When we divide 55 by 5 we get 11 as quotient that means 555=11

Therefore we got required answers 5 and 11 respectively.