Question

I am a 4-digit number exactly divisible by 25. My two middle digits are
the same and 1 is one of my digits. When 11 is added to me, I am exactly
divisible by 12. When 10 is subtracted from me, I am exactly divisible by
15. Who am I?​

Answer 1

Answer:

1225

Step-by-step explanation:

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Answer 2

The number is 1,225.

GIVEN

I am a 4-digit number exactly divisible by 25. My two middle digits are the same and 1 is one of my digits. When 11 is added to me, I am exactly

divisible by 12. When 10 is subtracted from me, I am exactly divisible by 15.

TO FIND

The number.

SOLUTION

We can simply solve the above problem as follows;

Let the number be ABCD

It is given that the number is exactly divisible by 25. This means that last two digits can be 00, 25, 50 or 75.

Let the number ends in 00

According to the condition;

The number formed is 1000.

Adding 11 to 1000 = 1011

Now, This number is not divisible by 12.

Therefore the number is not 1000.

Let the number ends in 25

The number formed is 1225

Adding 11 to 1225 = 1236

The number is divisible by 12

Subtracting 10 from 1225 = 1225-10 = 1215

Therefore the number is 1225.

Let the number ends in 50

The number formed is 1550

Adding 11 to 1550 = 1561

1561 is not divisible by 12.

Let the number ends in 75.

The number formed is 1775

Adding 11 to 1775 = 1786

This number is not exactly divisible by 12.

Hence, The number is 1,225

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