Question : 5 women and 9 girls earn a total of INR 18,720 in 9 days, while 9 women and 16 girls earn a total of INR 52, 080 in 14 days. How much will 12 women and 7 girls together earn (in INR) in 13 days?
Option 1: 42,510
Option 2: 41,990
Option 3: 42,380
Option 4: 42,120
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Correct Answer: 42,120
Solution :
Let a woman's and a girl's daily earnings be $x$ and $y$.
Given: 5 women and 9 girls earn INR 18,720 in 9 days, while 9 women and 16 girls earn 52, 080 in 14 days.
$9(5x+9y)=18720$...(i)
$14(9x+16y)=52080$...(ii)
Solving equations (i) and (ii)
$x=200, y=120$
Money earned by 12 women and 7 girls together in 13 days.
$=13(12x+7y)=13(12×200+7×120)=\text{INR}\;42,120$
Hence, the correct answer is 42,120.
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