Quantitative Aptitude - Arithmetic Ability Questions

Let Hari Ram's present age = x

Then, his son's age = x/3

Father's age = 5x/2

$$\begin{gathered} x + x3 + 52x3 = 46 \\ => x = 36 yrs \end{gathered}$$

Now the required difference = 52x36 - 363 = 78 yrs

Let us consider Karthik as K1 and Kalyan as K2.

Given k18+k1 and K2 - (K1 + 5) = 3 

K2 - K1 = 8

K2 = 8 + K1

Now, 

k18+k1= 45

=> K1 = 32 years

Therefore K2 = 40 years.

K1 + K2 = 72 years.

Let the list price be Rs.100. 

Therefore, the retailer is buying the products at Rs.60 and selling it to the customer at Rs.75, earning a profit of Rs.15.

Therefore, his percentage is = 1560x100 = 25%

For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9
Total number of zero in this range = 0

2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

Suppose total votes polled is x

Let the breadth of floor be 'b' m.

Then, length of the floor is 'l = (b + 25)'

Area of the rectangular floor = l x b = (b + 25) × b

According to the question,

(b + 15) (b + 8) = (b + 25) × b

b2 + 8b + 15b + 120 = b2 + 25b

2b = 120

b = 60 m.

l = b + 25 = 60 + 25 = 85 m.

Area of the floor = 85 × 60 = 5100 sq.m.

Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by K = 3 liters.
Capacity of tank filled in 1 minute by L = 15 liters.
Therefore, capacity of the tank filled by both K and L in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters = 8!/(2! x 2!)= 10080.

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =4!/2!= 12.

Required number of words = (10080 x 12) = 120960