# Exercise : 1

(b) 10 km/hr

(c) 12 km/hr

(d) 16 km/hr

(e) None of these

**Ans.e**

Distance covered by the car = 80 × 10 = 800 km

\ Speed = ^{800}⁄_{8} = 100 km/hr

\ Speed gain = 100 – 80 = 20 km/hr

(b) 24 minutes

(c) 32 minutes

(d) 36 minutes

(e) None of these

**Ans.c**

Speed of the car A = ^{5}⁄_{6} × 90 = 75 km/hr

\ Reqd time = \(\frac{88}{90 + 75} \times 60 = 32 \; minutes\)

(b) 5 am on the next day

(c) 5 pm on the next day

(d) 2 pm on the next day

(e) None of these

**Ans.b**

Distance covered by train A before the train B leaves

Mumbai Central = 60 × 3 = 180 km

\ Time taken to cross each other = ^{180}⁄_{12} = 15 hours

\Reqd time = 2pm + 15 = 5 am on the next day

^{1}⁄

_{4}hours

(b) 4

^{1}⁄

_{2}hours

(c) 4 hours 5 minutes

(d) Cannot be determined

(e) None of these

**Ans.b**

Distance covered in first two hours = 70 × 2 = 140 km

Distance covered in next two hours = 80 × 2 = 160 km

Distance covered in first four hours

140 + 160 = 300 km

Remaining distance = 345 – 300 = 45 km.

Now, this distance will be covered at the speed of 90 km/hr.

∴ Time taken = ^{45}⁄_{90} = ^{1}⁄_{2} hour.

Total time= 4 + ^{1}⁄_{2} = 4^{1}⁄_{2} hour.

(b) 12 km

(c) 6 km

(d) Data inadequate

(e) None of these

**Ans.d**

Let the distance between M and N and the speed of current in still water be d km and x km/hr respectively.

According to the question, \(\frac{d}{4 + x} + \frac{d}{4 - x} = 3\)

In the above equation we have only one equation but two variables, hence, can’t be determined.

(b) 72 km/hr

(c) 48 km/hr

(d) Data inadequate

(e) None of these

**Ans.d**

Let x be the speed of the boat.

and y the speed of the current.

In this equation there are two variables, but only one equation, so, the value of ‘x’ cannot be determined.

(b) 456 km

(c) 556 km

(d) 482 km

(e) None of these

**Ans.e**

This is the problem of arithmetic progression (AP) with the first term (a) = 35, common difference (d) = 2 and total no. of terms (n) = 12. The sum of this series will be total distance travelled.

Sum (S_{n}) = ^{n}⁄_{2}{2a + (n - 1)d} = ^{12}⁄_{2}{70 + 11 × 2}

= \(\frac{12 \times 92}{2} = 552 \; km\)

(b) 5 kmph

(c) 10 kmph

(d) Data inadequate

(e) None of these

**Ans.c**

Here downstream speed = 15 km/hr and upstream speed = 5 km/hr

∴ Speed of the boat = \(\frac{15 + 5}{2} = 10 \; km/h\)

(b) 6 km

(c) 12 km

(d) 8 km

(e) None of these

**Ans.b**

Required distance

= \(2\left[1 + \frac{2}{3} + \left(\frac{2}{3} \right)^{2} + \left(\frac{2}{3} \right)^{3} + .... \right]\)

= \(2 \times \frac{1}{1 - \frac{2}{3}} = 2 \times 3 = 6 \; km.\)

(b) 6

(c) 12

(d) 8

(e) None of these

**Ans.d**

Hour Speed (km/h) Distance travelled (in km)

Hence, the required time = 8 hours