Pradeep spends 40 percent of his monthly income on food items and 50 percent of the remaining, on cloths and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves Rs.19,200 every year, what is his monthly income?

Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.

2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.

? Ratio of speed = x/y : x/4y = 1 :1/4 = 4: 1

Speed of the train = (36 x 5)/18 = 10 m/sec.
Distance = (Time x Speed ) = (8 x 10 ) = 80 meters
? Length of the train = 80 meters

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

   = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Distance covered = (108 + 112) = 220 m.

⟹ 250 + 5x = 660

⟹ x = 82 km/hr.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x - 1) hours = 25(x - 1) km.

∴ 20x + 25(x - 1) = 110

⟹ 45x = 135

⟹ x = 3.

So, they meet at 10 a.m.

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Hence, S.P. = Rs. 25,300.

Since 653xy is divisible by 2 and 5 both, so y = 0.

Now, 653x is divisible by 8, so 13x should be divisible by 8.

This happens when x = 6.

∴x + y = (6 + 0) = 6.

(2n + 3)² - (2n + 1)² = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)

     = (4n + 4) x 2

     = 8(n + 1), which is divisible by 8.