6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?

A) 1/7	B) 8!
C) 7!	D) 1/14

Answer & Explanation Answer: D) 1/14

Explanation:

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14.

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Filed Under: Probability
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15 8640

Q:

What is the value of $100 P_{2}$ ?

A) 10000	B) 9900
C) 8900	D) 7900

Answer & Explanation Answer: B) 9900

Explanation:

Here in 100P2, P says that permutations and is defined as in how many ways 2 objects can be selected from 100 and can be arranged.

That can be done as,

$100 P_{2}$ = 100!/(100 - 2)!

= 100 x 99 x 98!/98!

= 100 x 99

= 9900.

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Filed Under: Permutations and Combinations
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8 8630

Q:

A fraction becomes 2/3 when 1 is added to both, its numerator and denominator .And , it becomes 1/2 when 1 is subtracted from both the numerator and denominator. What is the fraction?

Answer

Let required fraction be $\frac{x}{y}$ then

$\frac{x+1}{y+1}=\frac{2}{3}\Rightarrow 3x-2y=-1$ ............. (i)

and $\frac{x-1}{y-1}=\frac{1}{2}\Rightarrow 2x-y=1$ ............ (ii)

Solving (i) and (ii) we get x=3, y=5

$\inline \therefore$ Required fraction = $\frac{3}{5}$

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Subject: Problems on Numbers

16 8630

Q:

The price of 2 oranges, 3 bananas and 4 apples is Rs. 15. The price of 3 oranges, 2 bananas and 1 apple is Rs. 10. What will be price of 4 oranges, 4 bananas and 4 apples ?

A) Rs. 10	B) Rs. 15
C) Rs. 20	D) Rs. 25

Answer & Explanation Answer: C) Rs. 20

Explanation:

Let the Oranges be 'O', Bananas be 'B' and Apples be 'A'

From the given data,

2O + 3B + 4A = 15 ...... (I)

3O + 2B + A = 10 ..... (II)

On adding (I) and (II),

5O + 5B + 5A = 25

O + B + A = 5

4O + 4B + 4A = 20.

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Filed Under: Simplification
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12 8625

Q:

Three graziers A,B and C rent a piece of pasture for a month. A puts in 27 cattle for 19 days, B 21 for 17 days and C 24 for 23 days. If at the end of the month the rent amount to Rs.237, how much ought to be paid by each.

Answer

A's cattle = 27 x 19 = 513

B's cattle = 21 x 17 = 357

C's cattle = 24 x 23 = 552

Ratio of cattle = 513 : 357 : 552

= 171 : 119 : 184

payment to be made by A = $\inline 237\times \frac{171}{474}$

= Rs.85.50

payment to be made by B = $\inline 237\times \frac{119}{474}$

= Rs.59.50

payment to be made by C = $\inline 237\times \frac{184}{474}$

= Rs.92

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Subject: Partnership

7 8616

Q:

A sector of 120, cut out from a circle, has an area of $\frac{66}{7} c m^{2}$ . Find the radius of the circle ?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Let the radius of the circle be r cm. Then,

$\frac{120}{360} {πr}^{2} = \frac{66}{7}$

$r^{2} = \frac{66}{7} * \frac{7}{22} * 3$

r=3.

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Filed Under: Area
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2 8608

Q:

Ajay who is a King, at his eleventh hour, called his three queens and distributed his gold in the following way: He gave 50% of his wealth to his first wife, 50% of the rest to his second wife and again 50% of the rest to his third wife. If their combined share is worth1,30,900 kilograms of gold, find the quantity of gold King Ajay was having initially?

A) 153145 kgs	B) 147890 kgs
C) 152400 kgs	D) 149600 kgs

Answer & Explanation Answer: D) 149600 kgs

Explanation:

Let the total quantity of gold be p kgs.

According to the question,

50% of p + 25% of p + 12.5% of p = 130900

87.5% of p = 130900

p = 130900 x 100/87.5 = 149600 kgs.

Therefore, the initial gold quantity that king has = p = 149600 kgs.

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Filed Under: Percentage
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7 8607

Q:

$\frac{854 * 854 * 854 - 276 * 276 * 276}{854 * 854 + 854 * 276 + 276 * 276} = ?$

A) 546	B) 578
C) 607	D) None of these

Answer & Explanation Answer: B) 578

Explanation:

Given exp . is like this $\frac{854 * 854 * 854 - 276 * 276 * 276}{854 * 854 + 854 * 276 + 276 * 276} = ?$

so ans = 854 - 276 = 578

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Filed Under: Numbers

3 8605

Quantitative Aptitude - Arithmetic Ability Questions

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