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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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