The total salary of 15 men and 8 women is Rs. 3050. The difference of salaries of 5 women and 3 men is Rs. 50. Find the sum of the salaries of 3 men and 3 women.

Given, the total salary of

15

men and

8

women is

Rs . 3050

.
The difference of salaries of

5

women and

3

men is

Rs . 50

.
Let the salary of

1

man be Rs

x

and the salary of

1

woman be Rs.

y .

⇒

15 x + 8 y = 3050 . . . (1)

3 x - 5 y = - 50 . . . (2)

Multiply equation

(2)

5

,
⇒

15 x - 25 y = - 250 . . . (3)

Subtract equation

(3)

from equation

(1),

⇒

(15 x + 8 y) - (15 x - 25 y) = 3050 - (- 250)

\Rightarrow 15 x + 8 y - 15 x + 25 y = 3050 + 250

\Rightarrow 33 y = 3300

\Rightarrow y = 100

Substitute the value of

y

in equation

(2),

3 x - 500 = - 50

\Rightarrow 3 x = 450

\Rightarrow x = 150

Now, total salary of

3

men and

3

women will be,

3 x + 3 y = 3 \times 150 + 3 \times 100

⇒

3 x + 3 y = 450 + 300

⇒

3 x + 3 y = 750

Hence, the correct option is 2.

The total salary of $15$ men and $8$ women is $Rs . 3050$ . The difference of salaries of $5$ women and $3$ men is $Rs . 50$ . Find the sum of the salaries of $3$ men and $3$ women.