Question

Mrs. X spends Rs. 535 in purchasing some shirts and ties for her husband. If shirts cost Rs. 43 each and the ties cost Rs.21 each, then what is the ratio of the shirts to the ties, that are purchased ?

• A. 1 : 2
• B. 2 : 1
• C. 2 : 3
• D. 3 : 4

Answer 1

The Correct Option is B

To find the ratio of shirts to ties purchased by Mrs. X, we need to establish two equations based on the total cost and use the individual costs of shirts and ties: 

Let the number of shirts be \( x \) and the number of ties be \( y \).

Given:

\[ 43x + 21y = 535 \]

This is the equation derived from the total cost spent by Mrs. X. We want to find the ratio \( \frac{x}{y} \).

We will try to solve the equation to express \( x \) in terms of \( y \):

\[ 43x = 535 - 21y \]

Then, we express \( x \):

\[ x = \frac{535 - 21y}{43} \]

\( x \) must be an integer, so \( 535 - 21y \) must be divisible by 43. Let's test different values of \( y \) to find a solution where \( 535 - 21y \) yields an integer \( x \).

Check for a suitable \( y \):

\( y = 5 \)	\( 535 - 21 \times 5 = 535 - 105 = 430 \)
	\( x = \frac{430}{43} = 10 \)

This gives \( x = 10 \) and \( y = 5 \).

Thus, the ratio of shirts to ties is:

\[ \frac{x}{y} = \frac{10}{5} = \frac{2}{1} \]

The ratio of the shirts to the ties, therefore, is \( 2 : 1 \).