AIEEE Questions and Answers with Explanation

Q:

A contractor undertakes to complete a work in 130 days. He employs 150 men for 25 days and they complete 1/4 of the work . He then reduces the number of men to 100, who work for 60 days, after which there are 10 days holidays.How many men must be employed for the remaining period to finish the work?

Answer

150 men in 25 days do = $\frac{1}{4}$ work

Let 1 man in 1 day does = x work

Total work done by 150 men in 25 days = 150x * 25 = $\frac{1}{4}$ work => x = $\frac{1}{15000}$

Therefore, 100 men in 60 days do = 100 * 60x = 6000x work = 6/15 = 2/5

Total work done = $\frac{1}{4} + \frac{2}{5} = \frac{13}{20}$

Therefore, Remaining work = 1 - $\frac{13}{20}$ = $\frac{7}{20}$

Remaining time = 130 - (25+60+10) = 35 days

Therefore, work is done in 25 days by 150 men.

Therefore, Work is done in 35 days by 150 men.

Hence, he should employ 50 more men.

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Subject: Time and Work Exam Prep: Bank Exams , AIEEE
Job Role: Bank PO

44 16614

Q:

A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?

Answer

Let the average after 7th inning = x

Then average after 16th inning = x - 3

16(x-3)+87 = 17x

x = 87 - 48 = 39

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Subject: Average Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

659 91483

Q:

The value of

$\left [ \frac{2^{n}+2^{n-1}}{2^{n+1}-2^{n}} \right ]$ is:

Answer

$\frac{2^{n} + \frac{2^{n}}{2}}{2 x 2^{n} - 2^{n}} = \frac{2^{n} (1 + \frac{1}{2})}{2^{n} (2 - 1)} = \frac{3}{2}$

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Subject: Numbers Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Analyst , Bank Clerk , Bank PO

20 2883

Q:

(51 + 52 + 53 + .........+100) is equal to

Answer

51 + 52 + 53 + ...........+ 100

= (1 + 2 + 3 + .... + 100) - (1 + 2 + 3 + ...... + 50)

= It is in the form of $\frac{n (n + 1)}{2} s e r i e s s u m m a t i o n$

= n1 = 100 , n2 = 50

= $[\frac{100 (100 + 1)}{2}] - [\frac{50 (50 + 1)}{2}]$

= (5050 - 1275) = 3775

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Subject: Numbers Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

291 58016

Q:

The total number of prime factors in the expansion

$4^{11}\times 7^{5}\times11^{2}$

Answer

$2^{2^{11}} x 7^{5} x 11^{2} = > 2^{22} x 7^{5} x 11^{2}$

Total number of prime factors is (22+5+2) = 29

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Subject: Numbers Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Analyst , Bank Clerk , Bank PO

4 4688

Q:

Simplify the following equation.

$\frac{19}{43} + \frac{1}{(2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{4}}})}$

A) 43/19	B) 1
C) 38/19	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

After solving we get,

62/931.

None of the options satisfy.

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Filed Under: Simplification
Exam Prep: CAT , Bank Exams , AIEEE
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23 34251

Q:

Simplify

$\frac{1 . 5^{3} + 4 . 7^{3} + 3 . 8^{3} - 3 x 1.5 x 4.7 x 3.8}{1 . 5^{2} + 4 . 7^{2} + 3 . 8^{2} - 1.5 x 4.7 - 4.7 x 3.8 - 1.5 x 3.8}$

A) 6	B) 8
C) 10	D) 12

Answer & Explanation Answer: C) 10

Explanation:

Apply $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a} = a + b + c$

Hence the answer is 1.5 + 4.7 + 3.8 = 10.

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Filed Under: Simplification
Exam Prep: AIEEE , Bank Exams , CAT
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33 70640

Q:

Simplify and find '?'

$48 \sqrt{?} + 32 \sqrt{?} = 320$

A) 4	B) 8
C) 16	D) 32

Answer & Explanation Answer: C) 16

Explanation:

given

$48 \sqrt{?} + 32 \sqrt{?} = 320$

=> $6 \sqrt{?} + 4 \sqrt{?} = 40$

Now squaring on both sides

=> $36 x ? + 16 x ? + 48 x ? = 1600$

=> 100 x ? = 1600

=> ? = 16

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Filed Under: Simplification
Exam Prep: AIEEE , Bank Exams , CAT
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14 30803

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