X, Y and Z together earn ₹2,400/- in 15 days. X and Y together earn ₹1,840/- in 16 days. Y and Z together earn ₹1,530/- in 18 days. What is the daily earning (in ₹) of Y?

Correct option is A

Given:

X, Y, and Z together earn ₹2,400 in 15 days.

X and Y together earn ₹1,840 in 16 days.

Y and Z together earn ₹1,530 in 18 days.

Solution:

Let's denote the daily earnings of X, Y, and Z as , and respectively.

The total earnings of X, Y, and Z in 15 days is ₹2,400. Therefore, 

​$$15(x+y+z)=2400$$ 

$$x + y + z = \frac{2400}{15} = 160$$ .......(Eq.1)

The total earnings of X and Y in 16 days is ₹1,840. Therefore, 

$$16(x + y) = 1840$$

$$x + y = \frac{1840}{16} = 115$$ .........(Eq.2)

The total earnings of Y and Z in 18 days is ₹1,530. Therefore,

$$18(y + z) = 1530$$

$$y + z = \frac{1530}{18} = 85$$ ........(Eq.3)

subtract equation (2) from equation (1):

$$(x + y + z) - (x + y) = 160 - 115$$

$$z = 45$$

Now substitute z=45 into equation (3):

$$y + 45 = 85$$

$$y = 85 - 45 = 40$$

Thus the daily earning of Y is 40.