Question:medium

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

Updated On: Jan 15, 2026
Show Solution

Correct Answer: 35

Solution and Explanation

Let \( x \) be the number of patients admitted to hospital A, and \( x + 21 \) be the number of patients admitted to hospital B.

Given information:

  • Total recovery days for hospital A: 200
  • Total recovery days for hospital B: 152
  • Average recovery days for hospital A is 3 days more than for hospital B.

Step 1: Formulate the Equation

Average recovery days for hospital A = \( \frac{200}{x} \)

Average recovery days for hospital B = \( \frac{152}{x + 21} \)

The problem states that the average for hospital A exceeds the average for hospital B by 3 days. This yields the equation:

\[ \frac{200}{x} = \frac{152}{x + 21} + 3 \]

Step 2: Solve the Equation

Isolate the terms with \( x \):

\[ \frac{200}{x} - \frac{152}{x + 21} = 3 \]

To eliminate the denominators, multiply both sides by \( x(x + 21) \):

\[ 200(x + 21) - 152x = 3x(x + 21) \]

Expand both sides of the equation:

\[ 200x + 4200 - 152x = 3x^2 + 63x \]

Combine like terms:

\[ 48x + 4200 = 3x^2 + 63x \]

Rearrange into a standard quadratic form \( ax^2 + bx + c = 0 \):

\[ 3x^2 + 15x - 4200 = 0 \]

Apply the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 3 \), \( b = 15 \), and \( c = -4200 \).

Substitute the values:

\[ x = \frac{-15 \pm \sqrt{15^2 - 4(3)(-4200)}}{2(3)} \]

Calculate the discriminant:

\[ x = \frac{-15 \pm \sqrt{225 + 50400}}{6} \]

\[ x = \frac{-15 \pm \sqrt{50625}}{6} \]

Calculate the square root:

\[ x = \frac{-15 \pm 225}{6} \]

Determine the possible values for \( x \):

  • Solution 1 (using +): \[ x = \frac{-15 + 225}{6} = \frac{210}{6} = 35 \]
  • Solution 2 (using -): \[ x = \frac{-15 - 225}{6} = \frac{-240}{6} = -40 \quad \text{(Invalid as the number of patients cannot be negative)} \]

Step 3: Final Answer

The number of patients admitted to hospital A is \( \boxed{35} \).

Was this answer helpful?
0

Top Questions on Average

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution