Question

Amrit thought a two digits number which is six times the sum of the digits.

If 9 is subtracted from the number thought by Amrit, the digits are reversed. Find
the number thought by him.

Answer 1

To find the number thought by Amrit, we set up an equation based on the given information and solve for the possible values of a and b. By checking each possibility, we find that the number thought by Amrit is 32.

Step-by-step explanation:

Let the two-digit number be 10a + b, where a and b are the digits.

According to the given information, the number thought by Amrit is 6 times the sum of its digits:

1. 10a + b = 6(a + b)
2. 10a + b = 6a + 6b
3. 4a = 5b

Since a and b are digits, the possible values for a are 1, 2, 3, 4, and the corresponding values for b are 4, 8, 2, 6.

We need to find the number thought by Amrit. Let's check each possible value:

1. If a = 1 and b = 4, the number is 10 + 4 = 14, and if we subtract 9 from it, we get 5 (the digits are not reversed).
2. If a = 2 and b = 8, the number is 20 + 8 = 28, and if we subtract 9 from it, we get 19 (the digits are not reversed).
3. If a = 3 and b = 2, the number is 30 + 2 = 32, and if we subtract 9 from it, we get 23 (the digits are reversed).
4. If a = 4 and b = 6, the number is 40 + 6 = 46, and if we subtract 9 from it, we get 37 (the digits are reversed).

Therefore, the number thought by Amrit is 32.

Learn more about Finding a two-digit number based on a given condition