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Quantitative Ability

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In how many different ways can the letters of the word 'OPTICAL' be arranged, so that the vowels always come together?

  1. 5040

  2. 720

  3. 120

  4. 840

  5. None of these


Correct Option: B
Explanation:

Treat all the vowels as a single letter, i.e. 'OIA'.

The 5 letters can be arranged in 5! ways.

The vowels can be arranged among themselves in 3! ways.

So, the  required number of ways = 5! * 3! = 720

In how many different ways can the letters of the word 'INSTITUTE' be arranged?

  1. 362880

  2. 72000

  3. 30240

  4. 90720

  5. None of these


Correct Option: C
Explanation:

The required number of ways = 9!/(3! * 2!) = 30240

In a class of 80 students, 50 students have 12 sweets each and 30 students have 20 sweets each. Find the average number of sweets per student.

  1. 15

  2. 16

  3. 38.4

  4. 17

  5. None of these


Correct Option: A
Explanation:

Total number of sweets = 50 * 12 + 30 * 20 = 1200

Average number of sweets with each student = 1200/80 = 15

The speed of a boat in still water is 15 kmph and the speed of the current is 3 kmph. A wind of speed 2 kmph is blowing in the opposite direction of the current. The distance travelled downstream in 15 minutes is

  1. 4 km

  2. 3.5 km

  3. 5 km

  4. 4.5 km

  5. None of these


Correct Option: A
Explanation:

The speed while going downstream = (15 + 3 - 2) kmph = 16 kmph

Distance = 16/4 = 4 km

 

Mr. Z spends 80% of his monthly income. He donates 50% of the remaining amount to an orphanage. If he still has Rs. 8000 left, what is his annual income?

  1. Rs. 960000

  2. Rs. 80000

  3. Rs. 96000

  4. Rs. 120000

  5. None of these


Correct Option: A
Explanation:

Money spent on donation = 50% of the remaining 20% = 10%

So, savings = 10%

Monthly income = 8000 * 100/10 = Rs. 80000

Annual income = 80000 * 12 = Rs. 960000

A box contains 20 electric bulbs, out of which 5 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is

  1. 1/4

  2. 17/38

  3. 21/38

  4. 3/38

  5. None of these


Correct Option: B
Explanation:

P (none of the balls is defective) = 15C2/20C2

                                                         = 21/38

P(at least one ball is defective) = 1 - 21/38

                                                    = 17/38

 

The numerator of a fraction is increased by 70% and the denominator is decreased by 10%. If the new fraction is 7/15, then find the original fraction.

  1. 7

  2. 7/55

  3. 77/255

  4. 21/85

  5. None of these


Correct Option: D
Explanation:

Let the original fraction be n/p.

 (1.7*n)/(0.9*p) = 7/15

So, n/p = 21/85

If an article is sold at Rs. 17500 after giving 30% discount, what is its marked price?

  1. Rs. 12250

  2. Rs. 5250

  3. Rs. 25000

  4. Rs. 7500

  5. None of these


Correct Option: C
Explanation:

Let the price be y.

Then, y - (y * 30/100) = 17500

7 * y/10 = 17500

y = 25000

The average weight of a class of 29 students is 35 kg. If the weight of the teacher is included, the average weight rises by 500 g. The weight of the teacher is

  1. 14.5 kg

  2. 50 kg

  3. 35.5 kg

  4. 70.5 kg

  5. None of these


Correct Option: B
Explanation:

Total weight (only students) = 35*29 = 1015 kg

Let the weight of the teacher be y.

Then, (1015 + y)/30 = 35.5

1015 + y = 1065

y = 50 kg

A, B and C hired a car for Rs. 780 and used it for 6, 9 and 11 hours, respectively. The hire charge paid by C is

  1. Rs. 330

  2. Rs. 270

  3. Rs. 180

  4. Rs. 600

  5. None of these


Correct Option: A
Explanation:

Hire charge paid by C = 11 x 780/(6 + 9 + 11)

                                       = 11 x 30 = 330

If the length of a rectangle is increased by 200% and the breadth is decreased by 40%, then find the change in the area of the rectangle.

  1. 120% increase

  2. 160% increase

  3. 80% decrease

  4. 80% increase

  5. None of these


Correct Option: D
Explanation:

Let the length be l and the breadth be b.

Then, new length = 3 * l and breadth = 0.6 * b

So, area = 1.8 * l * b

So, the increase is 80%.

A invested Rs. 76000 in a business. After a few months, B joined him with Rs. 57000. At the end of the year, the total profit was divided between them in the ratio 4 : 1. After how many months did B join?

  1. 8 months

  2. 4 months

  3. 39/4 months

  4. 3 months

  5. None of these


Correct Option: A
Explanation:

Let's say B joined after y months. 

Then, (76000 * 12)/(57000 * (12 - y)) = 4 : 1

48/(36 - 3 * y) = 4

12 = 36 - 3 * y

y = 8 months

The average age of 8 men is increased by 2 years when two of them with ages 21 and 23 years are replaced by two new men. The average age of the two new men is

  1. 30

  2. 60

  3. 22

  4. 44

  5. None of these


Correct Option: A
Explanation:

Total age increased = 8 * 2 = 16 years

Sum of the ages of two new men = 23 + 21 + 16 = 60 years

Average age of two new men = 60/2 = 30 years

The numerator of a fraction is decreased by 30% and the denominator is decreased by 40%. If the new fraction is 7/9, then find the original fraction.

  1. 2/3

  2. 98/117

  3. 3/4

  4. 7/12

  5. None of these


Correct Option: A
Explanation:

Let the original fraction be n/p.

Then, according to question, (0.7 x n)/(0.6 x p) = 7/9

n/p = 6/9 = 2/3

A sum of money is to be distributed among A, B, C and D in the proportion 5 : 3 : 4 : 2. If C gets Rs. 1000 more than D, what is B's share?

  1. Rs. 7000

  2. Rs. 1000

  3. Rs. 2000

  4. Rs. 1500

  5. None of these


Correct Option: D
Explanation:

Let the total amount be x.

Then, C's share = 4 * x/14

D's share = 2 * x/14

So, (4 * x/14) - (2 * x/14) = 1000

x = 7000

Now, B's share = 3 * 7000/14 = 1500 Option (4) is correct.

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