Question

3. Sneha did a math magic with her friend Kriti. She asked her to think of a two-digit number. Then she asked her to add the digits of the number and then multiply the sum by 5. She asked her to add 5 to the product and multiply the result by 2. Then she asked her to divide the result by 10 and to subtract the sum of the digits from this number. Sneha told Kriti that number left is 1. Kriti is amazed. Can you help Kriti to understand this magic?​

Answer 1

Solution :-

Let kirti think of a two digit number is (10x + y) .

now,

→ she asked to multiply Digits sum by 5 = 5(x + y) = product

now,

→ Add 5 to the product and multiply by 2 = 2*[5x + 5y + 5] = Result.

now,

→ Dividing result by 10 and subtract sum of digits = 1

A/q,

→ 2(5x + 5y + 5)/10 - (x + y) = 1

→ 5(x + y + 1)/5 - (x + y) = 1

→ (x + y + 1) - (x + y) = 1

→ x - x + y - y + 1 = 1

→ 1 = 1

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Answer 2

Given :  Sneha did a math magic with her friend Kriti.

She asked her to think of a two- digit number.

Then she asked her to add the digits of the number and then multiply the sum by 5.

She asked her to add 5 to the product and multiply the result by 2.

Then she asked her to divide the result by 10 and to subtract the sum of the digits from this number.

Sneha told Kriti that number left is 1.

Kriti is amazed.

To Find :  Can you help Kriti to understand this magic?

Solution:

a two- digit number can be  AB

where A can be any digit from 1 to 9

and B can be any Digit  from 0 to 9

add the digits of the number and then multiply the sum by 5

= (A + B) 5

=  5(A + B)

add 5 to the product and multiply the result by 2.

= (5(A + B) + 5) * 2

= (5 (A + B + 1)( * 2

= 10 (A + B + 1)  

divide the result by 10 and to subtract the sum of the digits from this number.

= (10 (A + B + 1) /10  )  - (A + B)

=  A + B + 1 - A - B

= 1

Hence Result is always 1 independent of values of A and B

Thats why Sneha could tell kirti that result is 1.

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