Question

The total monthly salary of 4 men and 2 women is 51000. If women earn 1500 more than man, what is the monthly salary of women?

• A. 6500
• B. 7500
• C. 8500
• D. 9500

Hint:

To check your answer quickly:
If woman's salary $W = 9500$, then man's salary $M = 9500 - 1500 = 8000$.
Calculate the total:
\[ 4(8000) + 2(9500) = 32000 + 19000 = 51000. \]
This confirms the answer is correct.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Word problems involving two unknown variables can be solved by translating the statements into system of linear equations.
We define variables for the unknowns, construct equations based on the given relationships, and use substitution or elimination to solve for the target variable.

Step 2: Detailed Explanation:
Let us define our variables:
- Let the monthly salary of a man be $M$.
- Let the monthly salary of a woman be $W$.
Now, translate the statements from the problem into mathematical equations:
1. Equation 1 (Total salary of 4 men and 2 women is 51000): \[ 4M + 2W = 51000 \] 2. Equation 2 (A woman earns 1500 more than a man): \[ W = M + 1500 \] This can be rewritten to express $M$ in terms of $W$: \[ M = W - 1500 \] 3. Solve for $W$ using substitution:
Substitute $M = W - 1500$ into Equation 1: \[ 4(W - 1500) + 2W = 51000 \] Expand the brackets: \[ 4W - 6000 + 2W = 51000 \] Combine the like terms: \[ 6W - 6000 = 51000 \] Add $6000$ to both sides: \[ 6W = 51000 + 6000 \] \[ 6W = 57000 \] Divide both sides by $6$: \[ W = \frac{57000}{6} \] \[ W = 9500 \] Therefore, the monthly salary of a woman is $\text{Rs. } 9500$.

Step 3: Final Answer:
The monthly salary of women is 9500.
Therefore, the correct option is (D).