Question

Two sewing masters Ramdeen and Ramsewak earn 15 and 20 per day respectively. Ramdeen stitches 6 shirts and 4 pants per day while Ram Sewak stiches 10 shirts and 4 pants per day. How many days should they work together to stich 60 shirts and 30 pants at Minimum cost if necessary.

Answer 1

Let total number of days they work together be $D$ and the total cost of stitching 60 shirts and 30 pants be $C$.

Now, Ramdeen earns Rs. 15 per day and Ramsewak earns Rs. 20 per day.

$\therefore$ Total earnings of Ramdeen = Rs. $D\times 15$

$\therefore$ Total earnings of Ramsewak = Rs. $D\times 20$

$\therefore$ Total cost of stitching 60 shirts and 30 pants = $C=D\times 20+D\times 15=D\times 35=35D$

Also if Ramdeen stitches 6 shirts and 4 pants per day while Ram Sewak stiches 10 shirts and 4 pants per day,

Total shirts stitched = $60=(10+6)\times D=16D$

$⟹D=\frac{15}{4}⟹D=4$ days

Total pants stitched $=30=(4+4)\times D=8D$

$⟹D=\frac{15}{4}⟹D=4$ days

Total cost for $4$ days $=35\times 4=140$

Hence, the minimum number of days they work together is $4$ and the total incurred cost is Rs. $140$.