6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

A) 43929	B) 59049
C) 15120	D) 0

Answer & Explanation Answer: A) 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed = $9^{5}$

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = $9 P_{5}$

Number of words can be formed which have at least one letter repeated = $9^{5} - 9 P_{5}$

= 59049 - 15120

= 43929

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Filed Under: Permutations and Combinations
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11 6316

Q:

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A) 126	B) 240
C) 120	D) 260

Answer & Explanation Answer: A) 126

Explanation:

There are 8 students and the maximum capacity of the cars together is 9.

We may divide the 8 students as follows

Case I: 5 students in the first car and 3 in the second Or

Case II: 4 students in the first car and 4 in the second

Hence, in Case I: 8 students are divided into groups of 5 and 3 in $8 C_{3}$ ways.

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in $8 C_{4}$ ways.

Therefore, the total number of ways in which 8 students can travel is

$8 C_{3} + 8 C_{4}$ = 56 + 70 = 126.

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Filed Under: Permutations and Combinations

0 6315

Q:

75% of 450 + ? % of 560 = 600

A) 52.385	B) 46.875
C) 42.155	D) 40.555

Answer & Explanation Answer: B) 46.875

Explanation:

75% of 450 + ? % of 560 = 600

$\frac{75 x 450}{100} + \frac{? x 560}{100} = 600 \frac{75 x 9}{2} + \frac{28 p}{5} = 600 \frac{75 x 9 x 5 + 56 p}{10} = 600 3375 + 56 p = 6000 56 p = 2625 p = 46.875$

Hence, in the given question ? = 46.875

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Filed Under: Percentage
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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4 6311

Q:

How many seconds will a 600 m long train take to cross a man walking with a speed of 7 km/hr in the direction of the moving train if the speed of the train is 67 km/hr ?

A) 29 sec	B) 58 sec
C) 36 sec	D) 44 sec

Answer & Explanation Answer: C) 36 sec

Explanation:

Speed of train relative to man = 67 - 7 = 60 km/hr.
= 60 x 5/18 = 50/3 m/sec.

Time taken to pass the man = 600 x 3/50 = 36 sec.

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Filed Under: Problems on Trains
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3 6305

Q:

What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5%

A) Rs. 2	B) Rs. 1.25
C) Rs. 2.25	D) Rs. 0.5

Answer & Explanation Answer: B) Rs. 1.25

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

$B D = \frac{F T R}{100} = \frac{8100 \times \frac{1}{4} \times 5}{100} = R s . 101.25$

$T D = \frac{F T R}{100 + T R} = \frac{8100 \times \frac{1}{4} \times 5}{100 + (\frac{1}{4} \times 5)} = R s . 100$

Therefore BD - TD = 101.25-100 = Rs.1.25

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Filed Under: Banker's Discount

1 6303

Q:

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is

A) Rs.1650	B) Rs.1550
C) Rs.1750	D) Rs.1850

Answer & Explanation Answer: C) Rs.1750

Explanation:

C.I. =Rs[4000x(1+10/100)²-4000]

Rs.(4000x11/10x11/10-4000) = Rs.940.

Sum

=Rs. [420 *100 /3 * 8]

= Rs.1750.

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Filed Under: Compound Interest
Exam Prep: Bank Exams
Job Role: Bank PO

3 6291

Q:

Namitha sold a powerbank which is at the cost of Rs. 1950 at a loss of 25%. Find at what cost will she have to sell it to get a profit of 25%?

A) Rs. 3680	B) Rs. 3560
C) Rs. 3320	D) Rs. 3250

Answer & Explanation Answer: D) Rs. 3250

Explanation:

Let the Cost price of the powerbank = Rs. P

But given that by selling it at Rs. 1950, it gives a loss of 25%

=> $\frac{P x 75}{100} = 1950$
=> $P = \frac{1950 x 100}{75}$ = Rs. 2600
Now, to get a profit of 25%

Selling Price = $\frac{2600 x 125}{100} = Rs . 3250$ .

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Filed Under: Profit and Loss
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15 6279

Q:

The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is

A) 7! x 7!	B) 7! x 6!
C) 6! x 6!	D) 7! x 5!

Answer & Explanation Answer: B) 7! x 6!

Explanation:

The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in $7 P_{6}$ ways. 7 teachers can sit in (7-1)! ways.

Required no.of ways is = $7 P_{6} . 6! = 7! . 6!$

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Filed Under: Permutations and Combinations
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10 6276

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