Question:medium

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

Updated On: Jan 15, 2026
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Solution and Explanation

Let the total work be \( 48 \) units. Let Amar's monthly work be \( m \), Akbar's monthly work be \( k \), and Anthony's monthly work be \( n \).

Step 1: Establishing the equations

Amar and Akbar together complete the project in \( 12 \) months. Their combined monthly work is: \[ \frac{48}{12} = 4 \, \text{units}. \] This yields the equation: \[ m + k = 4 \quad \text{…… (i)}. \] Similarly, for Akbar and Anthony: \[ k + n = 3 \quad \text{…… (ii)}. \] And for Amar and Anthony: \[ m + n = 2 \quad \text{…… (iii)}. \]

Step 2: Solving the system of equations

The system of equations is: \[ m + k = 4 \quad \text{(i)} \] \[ k + n = 3 \quad \text{(ii)} \] \[ m + n = 2 \quad \text{(iii)}. \] Solving these equations: - From equation (i), \( k = 4 - m \). - Substituting into equation (ii): \( (4 - m) + n = 3 \Rightarrow n = 3 - 4 + m \Rightarrow n = m - 1 \). - Substituting \( n = m - 1 \) into equation (iii): \( m + (m - 1) = 2 \Rightarrow 2m - 1 = 2 \Rightarrow 2m = 3 \Rightarrow m = \frac{3}{2} \). - Substituting \( m = \frac{3}{2} \) into \( k = 4 - m \): \( k = 4 - \frac{3}{2} = \frac{8}{2} - \frac{3}{2} = \frac{5}{2} \). - Substituting \( m = \frac{3}{2} \) into \( n = m - 1 \): \( n = \frac{3}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{1}{2} \).

Step 3: Time taken to complete the work

Amar completes \( \frac{3}{2} \) units of work per month. To complete the total 48 units of work, the time required is: \[ \text{Time} = \frac{48}{\frac{3}{2}} = 48 \times \frac{2}{3} = 16 \times 2 = 32 \, \text{months}. \]

Final Answer:

The time taken to complete the work is \( \boxed{32} \) months.

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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.
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