A shop sells only steamed momos and fried momos. On a particular day the ratio of the numbers of steamed momos and fried momos sold from that shop was 5 : 4. How many steamed momos were sold from the shop on that day?

Which one of the following is correct in respect of the Question and the Statements given below?

Statement 1: If the number of steamed momos were to double, the ratio of the numbers of steamed momos and fried momos sold from that shop would become 5 : 2.

Statement 2: If the number of fried momos sold was at least 13 more while the number of steamed momos sold stayed the same, then the number of fried momos sold would have been more than the number of steamed momos sold.

Correct option is B

Given:
The ratio of steamed momos to fried momos sold = 5 : 4.

Solution:

Statement 1: If the number of steamed momos were to double, the ratio of the numbers of steamed momos and fried momos sold from that shop would become 5 : 2.

Let the number of steamed momos sold be 5x, and the number of fried momos sold be 4x, where x is a common factor.

If the number of steamed momos were to double: 2 × 5x = 10x.

The ratio would become: $$\frac{10x}{4x} = 5 : 2$$

This statement does not provide a specific value for x.

So, Statement 1 alone is not sufficient to answer the question.

Statement 2: If the number of fried momos sold was at least 13 more while the number of steamed momos sold stayed the same, then the number of fried momos sold would have been more than the number of steamed momos sold.

Let the number of steamed momos sold be 5x, and the number of fried momos sold be 4x, where x is a common factor.

If the number of fried momos increases by 13,

The new number of fried momos would be 4x + 13. Then,

4x + 13 $$\geq$$​ 5x

13 $$\geq$$​ 5x - 4x

13 $$\geq$$​ x

It does not provide a specific value for x.

So, Statement 2 alone is not sufficient to answer the question.

Now let's consider both statements together:

Statement 1 only confirms the initial ratio and doesn't give a specific value for x.
Statement 2 gives us the inequality 13 $$\geq$$​ x.

This implies x can be any positive integer less than some value greater than or equal to 13.

There are multiple possible integer values for x (e.g., x = 1,2,...,12).

Since x is not uniquely determined

So, the data in Statement 1 and Statement 2 both taken together are not sufficient to answer the question.

Thus, the correct option is (b).