Question : 4 women and 7 men earn a total of INR 11,480 in 7 days, while 10 women and 17 men earn a total of INR 36,360 in 9 days. How much will 11 women and 9 men together earn (in INR) in 13 days?
Option 1: 42,770
Option 2: 42,640
Option 3: 42,510
Option 4: 42,900
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Correct Answer: 42,640
Solution :
Given: 4 Women and 7 men earn a total of INR 11,480 in 7 days.
10 women and 17 men earn a total of INR 36,360 in 9 days.
1-day income of 4 women and 7 men is $\frac{11480}{7} = 1640$
1-day income of 10 women and 17 men is $\frac{36360}{9} = 4040$
Let the women's earnings be $x$ and the men's be $y$.
So, $4x + 7y = 1640$ ------------------(1)
and $10x + 17y = 4040$ ------------------(2)
Substituting the value of $x$ from equation (1) in equation (2), we get,
$10\times(\frac{1640 - 7y}{4}) + 17y = 4040$
$⇒16400 - 70y + 68y = 16160$
$⇒16400 - 16160 = 2y$
$⇒2y = 240$
$⇒y = 120$
Putting the value of y in equation (1),
$4x + 7 × 120 = 1640$
$⇒4x + 840 = 1640$
$⇒x = 200$
11 women's income in 1 day is 11 × 200 = INR 2,200
So, 11 women's income in 13 days is 2200 × 13 = INR 28,600
9 men's income in 1 day is 9 × 120 = INR 1,080
So, 9 men's income in 13 days is 1080 × 13 = INR 14,040
The total income of 11 women and 9 men in 13 days is = 28600 + 14040 = INR 42,640.
Hence, the correct answer is 42,640.
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