Prasanna invested certain amount in three different schemes X, Y and Z with the rate of interest 10% p.a, 12% p.a and 15% p.a respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme Z was 150% of the amount invested in Scheme X and 240% of the amount invested in Scheme Y, what was the amount invested in Scheme Y by Prasanna ?

(?)² = ?13² + 28 / 4 - (3)³ + 107
= ?169 + 7 - 27 + 107
= ?256
= ?16
= 4

Let A takes x and B takes 3N days to finish the job.
According to the question,
3N - N = 30
? N = 30/2 = 15 days
? B's time to complete the work = 3N
= 3 x 15 = 45 days

? (A + B)'s 1 day's work
= (1/15) + (1/45) = (3 + 1)/45 = 4/45
? (A + B) will finish the work in 4/45 days
? Required time = 4/45 = 11¹/₄

Let 75% of 480 = A x 15.
? (75 x 480)/100 = 15A
? A = (75 x 480)/ (100 x 15) = 24

Given, downstream speed = 9 km/h
and upstream speed = 5 km/h

According to the formula
Ravi's speed in still water = (Speed downstream + Speed upstream )/2
= 1/2(9 + 5) = 14/2 = 7 km/h
and speed of current = (Speed downstream - Speed upstream)/2
= (9 - 5)/2 = 4/2 = 2 km/h.

Part filled by X in 1st min and Y in the 2nd min = ( 1/6 + 1/7) = 13/42
Part filled by ( X + Y ) working alternately in 6 min = 1/2 x 13/42 x 6 =13/14
? Remaining Part = ( 1- 13/14 ) = 1/14
Now, it is the turn of X, one-sixth part is filled in 1 min.
One-fourteenth part is filled in (6 x 1/14) min = 3/7
? Required time = ( 6 + 3/7 ) = 6³/₇ min

Time taken by A to fill the tank, m = 15 min
? Time taken by B to fill the tank, n = 15 x 4 = 60
? Required time taken m x n/(m + n)
= (15 x 60)/(15 + 60) = (15 x 60)/75 = 12 min