Question: What is the 3-digit number which is divisible by 10?

Statement-I: If the digits in hundred's place and ten's place of the number are interchanged, the resulting number is diminished by 180.

Statement-II: If the digit in hundred's place is halved and digit in ten's place and unit place of the number are interchanged, the resulting number is diminished by 336.

Question

Question

This question was previously asked in

CDS Elementary Mathematics 3 Sep 2023 Official Paper

if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
if the question can be answered by using either statement alone.
if the question can be answered by using both the statements together, but cannot be answered using either statement alone.
if the question cannot be answered even by using both the statements together.

Answer 1

Given:

A 3 digit number which is divisible by 10.

Calculation:

Let the three digit number be "xy0"

x = digit of hundred's place and y = digit of ten's place

According to Statement-1

When the digits of hundred's and ten's place interchanged, then

⇒ xy0 - yx0 = 180

⇒ (100x + 10y + 0) - (100y + 10x + 0) = 180

⇒ 90x - 90y = 180

⇒ x - y = 2 -----(1)

Statement-1 alone is not sufficient to get the values.

Now from Statement-2

Digit in hundred's place is halved and ten's and unit place interchanged,

⇒ xy0 - (x/2)0y = 336

⇒ (100x + 10y + 0) - (100x/2 + 10 × 0 + y) = 336

⇒ 100x + 10y - 50x - y = 336

⇒ 50x + 9y = 336 -----(2)

We got two linear equations using both the statement,

∴ Both statements are required to find the value of x and y.

∴ Question can be answered by using both the statements together.