Aptitude

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📘 Height-and-Distance
📘 series
📘 Time and Distance
📘 Time and Work
📘 Train

101. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

by
[A]. 1 hour
[B]. 2 hours
[C]. 3 hours
[D]. 4 hours
✅ The correct answer is option A.
Let the duration of the flight be x hours.

Then,
600
–
600
= 200

x
x + (1/2)

600
–
1200
= 200

x
2x + 1

x(2x + 1) = 3
2×2 + x – 3 = 0
(2x + 3)(x – 1) = 0
x = 1 hr.      [neglecting the -ve value of x]

103. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

by
[A]. 14 km
[B]. 15 km
[C]. 16 km
[D]. 17 km
✅ The correct answer is option C.
Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.

So,
x
+
(61 -x)
= 9

4
9

9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.

104. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

by
[A]. 35
[B]. 36 2 3
[C]. 37 1 2
[D]. 40
✅ The correct answer is option D.
Let distance = x km and usual rate = y kmph.

Then,
x
–
x
=
40
    2y(y + 3) = 9x ….(i)

y
y + 3
60

And,
x
–
x
=
40
    y(y – 2) = 3x ….(ii)

y -2
y
60

On dividing (i) by (ii), we get: x = 40.

106. A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

by
[A]. 17 6 km/hr 7
[B]. 25 km/hr
[C]. 30 km/hr
[D]. 35 km/hr
✅ The correct answer is option D.
Time taken = 1 hr 40 min 48 sec = 1 hr 40
4
min = 1
51
hrs =
126
hrs.

5
75
75

Let the actual speed be x km/hr.

Then,
5
x x
126
= 42

7
75

x =

42 x 7 x 75

= 35 km/hr.

5 x 126

107. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

by
[A]. 6 days
[B]. 10 days
[C]. 15 days
[D]. 20 days
✅ The correct answer is option B.
Work done by X in 4 days =

1
x 4

=
1
.

20
5

Remaining work =

1 –
1

=
4
.

5
5

(X + Y)’s 1 day’s work =

1
+
1

=
8
=
2
.

20
12
60
15

Now,
2
work is done by X and Y in 1 day.

15

So,
4
work will be done by X and Y in

15
x
4

= 6 days.

5
2
5

Hence, total time taken = (6 + 4) days = 10 days.

108. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

by
[A]. 35
[B]. 40
[C]. 45
[D]. 50
✅ The correct answer is option B.
Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.

Then, 4x + 6y =
1
and 3x + 7y =
1
.

8
10

Solving the two equations, we get: x =
11
, y =
1

400
400

1 woman’s 1 day’s work =
1
.

400

10 women’s 1 day’s work =

1
x 10

=
1
.

400
40

Hence, 10 women will complete the work in 40 days.

109. A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :

by
[A].9 1 days 3
[B]. 11 days
[C].12 1 days 4
[D].16 1 days 3
✅ The correct answer is option B.
(A’s 1 day’s work) : (B’s 1 day’s work) =
7
: 1   =   7 : 4.

4

Let A’s and B’s 1 day’s work be 7x and 4x respectively.

Then, 7x + 4x =
1
        11x =
1
        x =
1
.

7
7
77

A’s 1 day’s work =

1
x 7

=
1
.

77
11

110. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

by
[A]. 1 4
[B].1 10
[C].7 15
[D].8 15
✅ The correct answer is option D.
A’s 1 day’s work =
1
;

15

B’s 1 day’s work =
1
;

20

(A + B)’s 1 day’s work =

1
+
1

=
7
.

15
20
60

(A + B)’s 4 day’s work =

7
x 4

=
7
.

60
15

Therefore, Remaining work =

1 –
7

=
8
.

15
15