**Find solutions for all the questions at the end of each set:**

### Set A

1. The speed of a boat in still water is 15 km/hr and the speed of the current is 5 km/hr. the distance (in km) travelled by the boat downstream in 15 minutes is

(a) 4

(b) 5

(c) 6

(d) 8

2. The speed of a boat is still water is 10 km/hr. If covers upstream a distance of 45 km in 6 hours. The speed (in km/hr) of the stream is

(a) 2.5

(b) 3

(c) 3.5

(d) 4

3. A motorboat can run 18.5 km/hr in still water. If it covered 60 km upstream in 4 hours. Find the speed of current.

(a) 3

(b) 3.5

(c) 4

(d) 4.5

4. A motorboat, travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 hours. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 hours. The speed of the stream is

(a) 2 km/hr

(b) 3 km/hr

(c) 4 km/hr

(d) 5 km/hr

5. A boat goes 12 km downstream and comes back to the starting point in 3 hours. If the speed of the current is 3 km/hr, then the speed (in km/hr) of the boat in still water is

(a) 12

(b) 9

(c) 8

(d) 6

6. A motor-boat can travel at 10 km/hour in still water. It travelled 91 km downstream in a river and then returned to the same place taking altogether 20 hours. Find the rate of flow of river.

(a) 3 km/hr

(b) 4 km/hr

(c) 2 km/hr

(d) 5 km/hr

7. The speed of the current is 5 km/hour. A motorboat goes 10 km upstream and back again to the starting point in 50 minutes. The speed, in km/hour, of the motorboat in still water is

(a) 20

(b) 26

(c) 25

(d) 28

8. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Then the speed of boat in still water and the speed of water current are respectively.

(a) 4 kmph and 3 kmph

(b) 4.5 kmph and 0.5 kmph

(c) 4 kmph and 2 kmph

(d) 5 kmph and 2 kmph

9. A boy can swim in still water at a speed of 10 km/hr. if the speed of the current would have been 5 km/hr, then the boy could swim 60 km.

(a) upstream in 4 hours

(b) downstream in 12 hours

(c) upstream in 6 hours

(d) downstream in 4 hours

10. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long, 44m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is

(a) 2

(b) 1 ½

(c) 3

(d) 2 ½

Answers and Solution:

1. (b)

The speed of boat downstream = 15 + 5 = 20km/hr

so The distance downstream = speed downstream*time = 20*15/60 = 5km.

2. (a)

Let the speed of stream is x km/hr.

so the speed upstream = 10 – x km/hr

so The speed upstream*time = distance

so (10-x)*6 = 45

so x = 15/6 = 2.5 km/hr.

3. (b)

Speed downstream = 60/4 = 15 km/hr

so The speed of current = 18.5 – 15 = 3.5 km/hr

4. (c)

5. (b)

6. (a)

7. (c)

8. (b)

The speed downstream = 20/4 = 5 km/hr

The speed upstream = 24/6 = 4 km/hr

The speed of boat in still water = (5+4)/2 = 4.5 km/hr

The speed of current = (5-4)/2 = 0.5 km/hr

so The speed of boat and water current are 4.5 km/hr and 0.5 km/hr

9. (d)

speed downstream = 10+5 = 15 km/hr

speed upstream = 10-5 = 5 km/hr

so time taken to swim 60 km down stream = 60/15 = 4 hours

10. (a)

**Find solutions for all the questions at the end of each set:**

### Set B

1. A sum of money at 8% per annum compound interest becomes 37,791.36 in 3 years. The sum of money is

(a) Rs. 28000

(b) Rs. 30000

(c) Rs. 32000

(d) Rs. 33000

2. A sum of Rs. 12000 deposited at compound interest becomes double after 5 years. After 20 years, it will become

(a) Rs. 48000

(b) Rs. 96000

(c) Rs. 190000

(d) Rs. 192000

3.The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420. The simple interest on the same sum at the same rate and for the same time will be

(a) Rs. 380

(b) Rs. 400

(c) Rs. 350

(d) Rs. 375

4.A principal of Rs. 10,000 after 2 year compound annually, the rate of interest being 10% per annum during the first year and 12% per annum during the second year ( in rupees) will amount to:

(a) Rs. 12,000

(b) Rs. 12,350

(c) Rs. 12,500

(d) Rs. 12,320

5.A sum of money becomes double in 3 years at compound interest compounded annually. At the same rate, in how many years will it become four times of itself.

(a) 4

(b) 6

(c) 6.4

(d) 7.5

6. If a sum of money placed at compound interests, compounded annually, doubles itself in 5 years, then the same amount of money will be 8 times of itself in

(a) 25 years

(b) 20 years

(c) 15 years

(d) 10 years

7.The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is Rs. 48. Then the sum is

(a) Rs. 1000

(b) Rs. 1200

(c) Rs. 1500

(d) Rs. 2000

8.The difference between the compound interest and simple interest for the amount Rs. 5000 in 2 years is Rs. 32. The rate of interest is

(a) 5%

(b) 8%

(c) 10%

(d) 12%

9. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% perannum, is Rs. 1. Find the sum

(a) Rs. 630

(b) Rs. 620

(c) Rs. 625

(d) Rs. 635

10.The difference between the compound interest and simple interest on a certain sum of money at 10% per annum for 3 years is Rs. 500. The sum is

(a) Rs. 45000

(b) Rs. 50000

(c) Rs. 55000

(d) None of these

Answers and Solution:

1. (b)

A = p(1+r/100)^n

37791.36 = p(108/100)^3

p = Rs. 30000

2. (d)

sum of Rs.12000 becomes double after 5 years

so 2*12000 = 12000(1+r/100)^5

so 2 = (1+r/100)^5 ……..(i)

then after 20 years A = 12000(1+r/100)^20

so A = 12000((1+r/100)^5)^4 = 12000*2^4 = 192000

3. (b)

4. (d)

Amount = P(110/100)*(112/100) = 10000*11/10*112/100 = 12320

5. (b)

In 3 years 2 times

Let in years 4 times = 2^2 times

so n = 3*2 = 6 years

6. (c)

In 5 years 2 times

Let in n years 8 times = 2^3 times

so n = 5*3 = 15 years

7. (b)

Sum of money = difference(100/r)^2

= 48(100/20)^2 = 1200

8. (b)

Difference = pr^2/(100)^2

=> 32 = 5000(r)^2/(100)^2

r = 8%

9. (c)

10. (d)

D = pr^2(300+r)/(100)^3

500 = P(10)^2(300+10)/(100)^3

p = 16129