Quantitative Aptitude - Arithmetic Ability Questions

Given word is TRANSFORMER.

Number of letters in the given word = 11 (3 R's)

Required, number of ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together is

10! x 2!/3!

= 3628800 x 2/6

= 1209600

Given that, speed of thief motorcycle is x kmph .

Given that, policemen started chasing him after 4 hours and catches him in 4 hours.

Distance travelled by the thief in 4 + 4 = 8 hours is d = s t 

=> d = 8x kms

Distance covered by the police in 4 hours is

D = 4 x 40 = 160 kms

To catch the thief, distance covered by the thief is equal to distance covered by the police .

Therefore,

d = D

d = 8x = 160 

x = 160/8 = 20

x = 20 kmph

Hence, the speed of thief's motorcycle is 20 km/hr.

Let the total amount he had with = Rs. p

From the given data,

p - 38460 - 24468 = 28p/100

p - 28p/100 = 24468 + 38460

72p/100 = 62928

72p = 62928 x 100

p = 62928 x 100/72

p = 87400

Hence, the total amount he had = p = Rs. 87400.

Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are 

5 x 4 x 3 x 2 x 1 = 120.

Let the larger number be p

Then, smaller number = 1/6 x p = p/6

Given difference between two numbers = 25

p - p/6 = 25

5p/6 = 25

5p = 150

p = 30

Then, p/6 = 30/6 = 5

Hence, larger number = 30 and smaller number = 5 which makes the difference = 25.