A magician played a trick from a pack of 9 cards with digits 1 to 9 , he picked two cards and formed a two digit number by placing it next to each other. He gave a clue that the difference of the two digits is 3. then he interchanged the places of the two cards, He asked the children to find the original number if the sum of original number and the new number is 143.
Answers
Answer:
85(however this can 58 as well, since he gave the difference* and didn't specified the unit or tens's place). 85 or 58
Step-by-step explanation:
Let the original number be ab. In the same manner as we write 11 = 1(10) + 1, 56 = 5(10) + 6, 79 = 7(10) + 9 etc, we can write ab = a(10) + b = 10a + b.
Here,
difference of the two digits is 3
⇒ a - b = 3 ....(1)
Also, sum of original number and the new number is 143.
[when the digits interchanged new number is ba = 10b + a]
⇒ (10a + b) + (10b + a) = 143
⇒ 11a + 11b = 143
⇒ 11(a + b) = 143
⇒ a + b = 143/11 = 13 ...(2)
Adding (1) and (2):
a - b = 3
a + b = 13
2a = 16
a = 16/2 = 8
hence, 8 - b = 3 ⇒ 5 = b
Number is ab = 85
Given,
- The Difference of Two Digits = 3
After Interchanging Digits,
- The Sum of New Number and Orginal Number = 143
To Find,
- The Original Number
Solution,
Let's,
The First Digit = X
So,
The Second Digit = Y
So,
→ The Number
= 10 × (First Digit) + 1 × (Second Digit)
→ The Number
= 10 × X + 1 × Y
→ The Number
= 10X + Y
After Interchanging Digits,
The First Digit = Y
The Second Digit = X
So,
→ The Interchanged Number
= 10 × (First Digit) + 1 × (Second Digit)
→ The Interchanged Number
= 10 × Y + 1 × X
→ The Interchanged Number
= 10Y + X
The Sum of Number and Interchanged Number = 143
→ (10X + Y) + (10Y + X) = 143 •••(Given)
→ 10X + Y + 10Y + X = 143
→ 11X + 11Y = 143
→ 11 × (X + Y) = 143
→ X + Y = 143/11
→ X + Y = 13 •••(1)
The Difference of Digits = 3 •••(Given)
→ X - Y = 3 •••(2)
By Adding (1) and (2) ;
→ (X + Y) + (X - Y) = 13 + 3
→ X + Y + X - Y = 16
→ 2X = 16
→ X = 16/2
→ X = 8
→ X - Y = 3 •••(2)
→ 8 - Y = 3
→ 8 - 3 = Y
→ Y = 5
Required Answer,
The Number Can be 85 or 58