Question

find two 2 digit numbers such that their product is 900 the product of units digit is 30 and tens digit is 6​

Answer 1

Answer:

The numbers are 25 and 36.

Step-by-step explanation:

If we try to solve this using the algebraic equation, it would be messy and we won't be able to solve it.

Thus, we must find the factors of 900 such that, it satisfies the above conditions

Now, if we check the factors of 900 it is a long list from 1 to 30,

Thus, writing it all down will again be messy and difficult and time consuming as well.

So, let's solve it logically.

Now, the units digits multiply to 30

Now,

30 = 1 × 30

30 = 2 × 15

30 = 3 × 10

30 = 5 × 6

We know that, the units digit is been multiplied, so they have only single digit, So the only factor satisfying that is 6 and 5.

Again,

Tens digit multiplied will give us 6,

6 = 1 × 6

6 = 2 × 3

Here both can be possible because both are single digit's

So, the possible numbers will be (16, 65) (66, 15) (25, 36) and (35, 26)

Now, we are very close to the solution.

Here, there are 4 possibilities, and we would think ok so all these numbers are correct. But no, According to the Question, they should have a product of 900.

So,

16 × 65 = 1040

66 × 15 = 990

25 × 36 = 900

26 × 35 = 910

Thus,

The numbers are 25 and 36.

We check if this is correct,

Product of units digit = 30

6 × 5 = 30

30 = 30 (True)

Next,

Product of tens digit = 6

2 × 3 = 6

6 = 6 (True)

Product of numbers = 900

25 × 36 = 900

900 = 900 (True)

Thus, our answer is correct.

Hope it helped and you understood it........All the best