Section-1

3

2

2

1

6

2

3

1

The angle moved by hour hand in 8 hours = 30°× 8
= 240°

Angle difference in 1 minute between hour hand
and minute hand = (11/2)°

Angle difference in 48 minutes between hour hand
and minute hand
48 × (11/2)° = 264°

So minor angle between them = 264° – 240° = 24°
50% of 24° = 12°

Hence, 12° will increase in 12/(11/2) = 24/11
minutes.

1

Let the initial salaries of Sita, Gita and Mita be 5x,
6x and 7x respectively.

Then, in first year their salaries will be 5x × 1.2,
6x × 1.25 and 7x × 1.2 i.e., 6x, 7.5x and 8.4x
respectively.

In second year salaries of Sita and Mita will be
6x × 1.4 and 8.4x × 1.25 i.e., 8.4x and 10.5x
respectively.

In second year, salary of Gita = (8.4x + 10.5x)/2
= 9.45x

Hence, in second year the percentage increase in
salary of Gita = (9.45x – 7.5x)/7.5x × 100 = 26%.

4

2

From options:

Option (1): 26862 – 8 × 110 = 25982 (Not possible)

Option (2): 26862 – 8 × 100 = 26062 (Possible)

Since we have to find greatest possible average
speed, so we can leave option (3) and option (4).

Hence, the required greatest possible average
speed is 100 km/h.

3

3

27

Work done by Amal, Sunil and Kamal is in HP.

So time taken by Amal, Sunil and Kamal will be in
AP.

Let Amal complete the work in n days.

Then, Kamal will complete the work in 2n days
and Sunil will complete the work in (n + 2n)/2
= 1.5n days.

Ratio of time taken = n : 1.5n : 2n = 2 : 3 : 4

Ratio of work done = 1/2 : 1/3 : 1/4 = 6 : 4 : 3

Total units of work = 6 × 4 + 4 × 9 + 3 × 16 = 108

Hence, time taken by Sunil alone to complete the
work is 108/4 = 27 days.

20808

972

3

1

2

1

Number of non-repeating one digit numbers

= 1 × 9 = 9

Number of non-repeating two digit numbers

= 9 × 9 = 81

Number of non-repeating three digit numbers

= 9 × 9 × 8 = 648

Hence, total numbers = 9 + 81 + 648 = 738.

4

19