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**Answers :-**

*1. (b) Let the speed of boat in still water = x km/h*

* Speed of stream = y km/h*

* Speed of boat in the downstream, D = (x + y) km/h*

* Speed of boat in the upstream, U*

* = (x – y) km/h*

* distance to be covered = 18 km*

* D = x + y = 18 km/4h = 9/2 km/h ………….. (i)*

* U = x – y = 18km/ 12h = 3/2 km/h ………. (ii)*

* On solving (i) and (ii)*

* y =[(9/2 – 3/2) /2] = 1.5 km/hr.*

* Alternate:*

* Speed of stream = ½ (D – U)*

* Speed of boat = ½ (D + U)*

* Now, By using those above Formula’s*

* Speed of Stream*

* = (1/2) (9/2 – 3/2) = 1.5*

*2. (a) Note : for detailed solution check earlier*

* question.*

* Downstream speed, D = 20 km/ 1 hr. – 20 km/hr*

* Upstream speed, U = 20 km/ 2hr. = 10 km/hr*

* Speed of the boat in still water , x*

* = (D + U)/2*

* = (20 + 10)/2 = 30/2 = 15 km/hr.*

*3. (c) Speed of the Upstream, U*

* = 750/675 = 10/9 m/s*

* Time of downstream*

* = 15/2 minutes = 450 seconds*

* (Thus, boat will return in the downstream)*

* Speed of downstream, D = 750/450 m/s = 5/3 m/s.*

* Thus, Speed of man in still water = (D + U)/2*

* = (5/3 + 10/9)/2 = (15 + 10) /(2 × 9) = 25/18*

* m/s*

* = 25/18 × 18/5 = 5 km/hr.*

*4. (c) Speed of boat in still water, x*

* = 6 km/h*

* Let speed of the stream = y km/h*

* Downstream speed = (6 + y) km/h*

* Upstream speed =*

* 6 – y km/h*

* According to Question,*

* 3 [(Distance/6 + y) = (Distance/(6 – y)]*

* 3/(6 + y) = 1/(6 – y)*

* (6 + y) = (18 – 3y)*

* 4y = 12*

* y = 3*

* Thus, Speed of stream*

* = 3 km/h.*

*5. (b) Speed of upstream, U = 40/8 = 5 km/h*

* Speedo of Downstream, D*

* = 36/6 = 6 km/h*

* Speed of boat in still water, x = (D + U)/2*

* = (5 + 60)/2 = 11/2 = 5.5 km/h.*

*6. (c) Speed of man in still water, x = 5 km/h*

* Speed of currant, y*

* = 1 km/h*

* Speed of downstream*

* = x + y = 5 + 1 = 6 km/h.*

* Speed of upstream*

* = x – y= 5 – 1 = 4 km/h*

* According to the question,*

* D/6 + D/4 = 1*

* (2D + 3D)/12 = 1*

* 5D = 12*

* D = 12/5 = 2.4 km.*

*7. (c) Speed of motar boat in still water,*

* x = 36 km/h*

* Speed of upstream, U*

* = 56 km/(1 + 3/4) = 56 × 4/7 = 32 km/hr*

* According to the question,*

* x – y = U*

* 36 – y = 32*

* y = 4 km/h*

* Speed of Downstream, D*

* = x + y*

* = 36 + 4*

* = 40 km/h*

* Time taken to cover the distance downstream*

* = 56/40 h*

* 1 hours 24 minutes*

*8. (b) Speed of man in still water, x*

* = 9/2 km/hr*

* Let speed of stream = y km/h*

* Downstream speed*

* = (9/2 + y)*

* Upstream speed = (9/2 – y)*

* According to the question,*

* 2 [Distance/(9/2 + y)] = Distance/ (9/2 – y)*

* 2/ (9/2 + y) = 1/(9/2 – y)*

* (2 × 2) /(9 + 2y) = 2/(9 – 2y)*

* 2/(9 + 2y) = 1 / (9 – 2y)*

* 18 – 4y = 9 + 2y*

* 6y = 9*

* y = 9/6 = 3/2 = 1.5 km/h*

*9. (c) Since the ratio is given 36 : 5*

* Let the speed of boat in still water = 36 km/h.*

* and the speed of the stream = 5 km/h*

* Downstream speed = 41 km/h*

* Upstream speed = 31 km/h*

* Distance = Downstream speed ×*

* Downstream time = (41 × 31/6) km.*

* Upstream time*

* = Distance/ Upstream = [41 × (31/6)]/31 = (41 ×*

* 31)/6 × 3*

* = 41/6 = 6 hrs. 50 min.*

* Alternate:*

* V ∝ 1/T*

* V1*

* /V2 = T2/T1*

* = 36 + 5/(36 – 5) = x/(31/6)*

* x = 41/6 hours*

* = 6hrs . 50 min.*

*10. (d) Downstream speed of boat, D = 15 km/h*

* Upstream speed of boat, U = 9 km/h*

* Speed of boat in still water, x = (D + U)/2*

* = (15 + 9)/2 = 12 km/h*

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