Aptitude Questions With Answers for Time & Distance Problems 1

1)A train covers a distance in 50 min ,if it runs at a speed

of 48kmph on an average.The speed at which the train must run

to reduce the time of journey to 40min will be.

1. Solution::

Time=50/60 hr=5/6hr

Speed=48mph

distance=S*T=48*5/6=40km

time=40/60hr=2/3hr

New speed = 40* 3/2 kmph= 60kmph

2)Vikas can cover a distance in 1hr 24min by covering 2/3 of

the distance at 4 kmph and the rest at 5kmph.the total

distance is?

2. Solution::

Let total distance be S

total time=1hr24min

A to T :: speed=4kmph

diistance=2/3S

T to S :: speed=5km

distance=1-2/3S=1/3S

21/15 hr=2/3 S/4 + 1/3s /5

84=14/3S*3

S=84*3/14*3

= 6km

3)walking at ¾ of his usual speed ,a man is late by 2 ½ hr.

the usual time is.

3. Solution::

Usual speed = S

Usual time = T

Distance = D

New Speed is ¾ S

New time is 4/3 T

4/3 T – T = 5/2

T=15/2 = 7 ½

4)A man covers a distance on scooter .had he moved 3kmph

faster he would have taken 40 min less. If he had moved

2kmph slower he would have taken 40min more.the distance is.

4.Solution::

Let distance = x m

Usual rate = y kmph

x/y – x/y+3 = 40/60 hr

2y(y+3) = 9x ————–1

x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

divide 1 & 2 equations

by solving we get x = 40

5)Excluding stoppages,the speed of the bus is 54kmph and

including stoppages,it is 45kmph.for how many min does the bus

stop per hr.

5.Solution::

Due to stoppages,it covers 9km less.

time taken to cover 9 km is [9/54 *60] min = 10min

6)Two boys starting from the same place walk at a rate of

5kmph and 5.5kmph respectively.wht time will they take to be

8.5km apart, if they walk in the same direction

6.Solution::

The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph

Distance between them is 8.5 km

Time= 8.5km / 0.5 kmph = 17 hrs

7)2 trains starting at the same time from 2 stations 200km

apart and going in opposite direction cross each other ata

distance of 110km from one of the stations.what is the ratio of

their speeds.

7. Solution::

In same time ,they cover 110km & 90 km respectively

so ratio of their speed =110:90 = 11:9

8)Two trains start from A & B and travel towards each other at

speed of 50kmph and 60kmph resp. At the time of the meeting the

second train has traveled 120km more than the first.the distance

between them.

8. Solution::

Let the distance traveled by the first train be x km

then distance covered by the second train is x + 120km

x/50 = x+120 / 60

x= 600

so the distance between A & B is x + x + 120 = 1320 km

9)A thief steals a ca r at 2.30pm and drives it at 60kmph.the

theft is discovered at 3pm and the owner sets off in another car

at 75kmph when will he overtake the thief

9. Solution::

Let the thief is overtaken x hrs after 2.30pm

distance covered by the thief in x hrs = distance covered by

the owner in x-1/2 hr

60x = 75 ( x- ½)

x= 5/2 hr

thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm

10)In covering distance,the speed of A & B are in the ratio

of 3:4.A takes 30min more than B to reach the destion.The time

taken by A to reach the destinstion is.

10. Solution::

Ratio of speed = 3:4

Ratio of time = 4:3

let A takes 4x hrs,B takes 3x hrs

then 4x-3x = 30/60 hr

x = ½ hr

Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

Modal Paper For Aptitude

1) The average ages of three persons is 27 years. Their ages are in the proportion of 1:3:5.What is the

age in years of the youngest one among them.

Sol: Let the age of three persons be x, 3x and 5x

-- >   9x/3 = 27 -- > x = 9

2) The average of 11 numbers is 50. If the average of first 6 numbers is 49 and that of last  6 is 52.Find

the 6th number.

Sol: The total sum of 11 results = 11 * 50 = 550

The total sum of first 6 results = 6 * 49 = 294

The total sum of last 6 results = 6 * 52 = 312

Sixth result = 294 + 312 – 550 = 56

3) Find L.C.M of 852 and 1491.

852) 1491 (1

852

639) 852 (1

639

213) 639 (3

639

0

H.C.F of 852 and 1491 is 213

: . L.C.M = 852*1491/213 = 5964

4) The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by

14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.

: . Required number = (L.C.M of 20, 25, 35, 40) – 6

= 1400-6 = 1394

5) The least multiple of 7 which leaves a remainder 4 when divided by 6,9,15 and 18   is

L.C.M of 6,9,15 and 18 is 90.

Let x be the least multiple of 7, which when divided by 90 leaves the remainder 4.

Then x is of the form 90k + 4.

Now, minimum value of k for which 90k + 4 is divisible by 4.

: . x = 4 * 90 + 4 = 364

6) Sum of three even consecutive numbers is 48, and then least number is

1)       16

2)       18

3)       20

4)       14

Sol: 4) Let the numbers be 2n, 2n+2 and 2n+4

2n + (2n+2) + (2n+4) = 48

6n = 48-6 = 42, n = 7

Hence the numbers are   -- > 14, 16 and 18

The least number is 14.

7) It being given that v 15 = 3.88, the best approximation to    v5/3 is

1)       0.43

2)       1.89

3)       1.29

4)       1.63

__    ___                 __     __         __

Sol: 3) x =    v5/3    = v5*3/3*3   =   v15 /v 9   =   v15/3   = 3.88/3 = 1.29

8)   Of the two-digit numbers (those from 11 to 95, both inclusive) how many have a Second digit

greater than the first digit?

1)       37

2)       38

3)       36

4)       35

Sol: 3) 12 to 19 -- > 8

23 to 29 -- > 7

34 to 39 -- > 6

45 to 49 -- > 5

56 to 59 -- > 4

67 to 69 -- > 3

78 to 79 -- > 2

89 -- > 1

9) The Value of v24 + 3v64 + 4v28 is

Sol: 24*1/2 + 43*1/3 + 28*1/4

-- > 4 + 4 + 4 -- > 12

10) 3 ¼ - 4/5 of 5/6 / 4 1/3 / 1/5 – ( 3/10 + 21 1/5 ) is equal to

Sol:    13/4 – 4/5 * 5/6 / 13/3 / 1/5 – ( 3/10 + 106/5 )   (use BODMASRULE)

-- > 13/4 – 4/6 / 13/3 / 1/5 – 215/10   -- > 31/12 / 13/3 * 5 – 215/10

-- > 31/12 / 65/3 – 43/2   -- > 31/12 / 130 – 129/6 -- > 31/12/1/6 = 31/12   * 6/1

-- > 31/2 = 15 1/2

1) 13 sheeps and 9 pigs were bought for Rs. 1291.85.If the average price of a sheep be  Rs. 74. What

is the average price of a pig.

Sol: Average price of a sheep = Rs. 74

: . Total price of 13 sheeps

= (74*13) = Rs. 962

But, total price of 13 sheeps and 9 pigs

= Rs. 1291.85

Total price of 9 pigs

= Rs. (1291.85-962) = Rs. 329.85

Hence, average price of a pig

=   (329.85/9) = Rs. 36.65

12) A batsman in his 18th innings makes a score of 150 runs and there by increasing his Average by 6.

Find his average after 18th innings.

Sol: Let the average for 17 innings is x runs

Total runs in 17 innings = 17x

Total runs in 18 innings = 17x + 150

Average of 18 innings = 17x + 150/18

: . 17x + 150/18 = x + 6 -- > x = 42

Thus, average after 18 innings = 42

13) . Find the H.C.F of 777 and 1147.

777) 1147 (1

777

370) 777 (2

740

37) 370 (10

370

0

: . H.C.F of 777 and 1147 is 37.

14) The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 210 the Other is

The other number

= L.C.M * H.C.F/given number

= 2310*30/210 = 330

15) The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, The average of

remaining numbers is?

Total of 50 numbers = 50 * 38 = 1900

Average of 48 numbers = 1900-(45+55) / 48

= 1800 / 48 = 37.5

16) Divide 50 in two parts so that the sum of reciprocals is (1/12), the numbers are

1)       20,30

2)       24,36

3)       28,22

4)       36,14

Sol: 1) Let the numbers be x and y then

X+y = 50. ………(i)

1/x + 1/y = 12

1/x + 1/50-x = 1/12..From (i) y = 50 – x

-- > 50-x+x/x(50-x) = 1/12

-- > x2-50x+600 = 0

-- > (x-30) (x-20) = 0

&am

Aptitude Material

1) Five years ago the average age of a family of 3 members was 27 years. A child has Been born, due

to which the average age of the family is 25 years today. What is the Present age of the child?

Sol: Average age of the family of 3 members

5 years ago = 27 years

Sum of the ages of the 3 members now

= (27 + 5) * 3 = 96 years

Average age of the family of 4 members now

= 25 years

Sum of the ages of the 4 numbers now

= 25*4 = 100 years

Age of child = 100 – 96 = 4 years

2) In a class of 20 students in an examination in Mathematics 2 students scored 100  Marks each, 3 get

zero each and the average of the rest was 40. What is the average Of the whole class?

Sol: Total marks obtained by a class of 20 students

= 2 * 100 + 3 * 0 + 15 * 40

= 200 + 600 = 800

: Average marks of whole class = 800/20 = 40

3). The greatest number, which can divide 432, 534 and 398 leaving the same remainder 7 in each, is

Required number is the H.C.F of

(432-7), (534-7) and (398-7)

i.e., H.C.F. of 425, 527, 391

Required number = 17

4) The sum of two numbers is 216 and their H.C.F is 27. The numbers are

.   Let the numbers be 27a and 27b

Then 27a + 27b = 216

a+b = 8

Value of co-primes a and b are (1,7) (3,5)

: . Numbers are (27*1, 27*7) = (27,189)

5) The greatest number of 4 digits which is divisible by each one of the number 12,18,21 and 28 is

Greatest number of 4 digits is 9999

L.C.M of 12, 18, 21, 28 = 252

On dividing 9999 by 252, the remainder is 171

: . Required number is (9999-171) = 9828

6) Four prime numbers are arranged in ascending order according to their magnitude.Product of first

three is 385 and the product of last three is 1001. The greatest number is.

1)       11

2)       13

3)       17

4)       19

Sol: 2) 385) 1001(2

770

231) 385(1

231 (1

154)231(1

154

77) 154(2

154

0

Hence the product of the middle terms = 77

Greatest prime number = 1001 / 77 = 13.

7) If the square root of 55625 is 75, then

____        ____        ______

v5625 + v56.25 + v0.5625 is equal to

1)       82.25

2)       83.25

3)       80.25

4)       79.25

____                _____              ______

Sol: 2) v5625   = 75; v56.25 = 7.5; v. 5625   = .75

-- > 75+7.5+0.75 = 83.25

8)   Which of the following integers has most number of divisors?

1)       176

2)       182

3)       99

4)       101

Sol: 2) 176 = 2,4,8,11,16,22,44,88

182 = 2,7,13,14,26,91

99 = 3, 9, 11, 33

101= 101

9) 10) A boy was asked to find the value of 3/8 of a sum of money. Instead of multiplying The sum by

3/8 he divided it by 3/8 and then his answer exceeded by Rs. 55. Find the Correct be x.

Sol: Let amount be x

8/3* - 3/8 * = 55

-- > 64x – 9x/24 = 55 -- > 55x/24 = 55

-- > x = 24*55/55 = 24

: . 3/8 of x = 3/8 * 24 = Rs.9

10) A boy was asked to find the value of 7/12 of a sum of money. Instead of multiplying The sum by

7/12 he divided it by 7/12 and thus his answer exceeded the correct Answer By Rs.95. Find the correct

answer.

Sol: Let sum = Rs. K

: . 12/7 k – 7k/12 = 95

-- > 144k – 49k/84   = 95 -- > k = 84

:.   7/12 k -- > 7/12 * 84 = Rs. 49

11) In a boat 25 persons were sitting. Their average weight increased one kilogram when One man

goes and a new man comes in. The weight of the new man is 70kgs. Find the Weight of the man who is

going.

Sol: Weight increased per person is 1 kg.

Total increase in weight = 25 kgs

Weight of new man is 70 kgs,

(Which means his weight is 25 kgs heavier)

The weight of the old man was 70 – 25 = 45 kgs

13) What is the greatest possible length that can be used to measure exactly the following Lengths 7m,

3m 85cm, 12m 95cm?

The length to be measured is

700cm, 385cm, 1295cm.

The required length in cm is the H.C.F of 700, 385, and 1295, which is 35 cm.