# Simplification

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.

1. b – [b -(a+b) – {b – (b – a+b)} + 2a] = ?

A. 0

B. 4a

C. a

D. -2a

Ans: Option A

Explanation:

= b – [b -(a+b) – {b – (b – a+b)} + 2a]

= b – [b -a -b – {b -b +a -b} + 2a]

= b – [b -a -b – {a -b} + 2a]

= b – [b -a -b – a +b + 2a]

= b – [b]

= b – b

= 0

2.  David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

A. 19

B. 28

C. 30

D. 37

Ans: Option A

Explanation:

Suppose their paths cross after x minutes.

Then, 11 + 57x = 51 – 63x

120x = 40

x = 1/3

Number of floors covered by David in (1/3) min = (1/3)x57=19

So, their paths cross at (11 +19) i.e., 30th floor.

3.  A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

a) 36

b) 24

c) 28

d) 32

Ans: Option A

Explanation:

Let the number of notes of each denomination be x

Then, x + 5x + 20x = 312

26x = 312

So, x = 312/26 = 12

The total number of notes that he has = 3x = 3 × 12 = 36

4. (31/10) * (3/10) + (7/5) / 20

A. 0

B. 107/200

C. 100

D. 1

Ans: Option D

Explanation:

No explanation

5. An organization decided to raise Rs. 6 lakh by collecting equal contribution from each of its employees. If each of them had contributed Rs. 60 extra, the contribution would have been Rs. 6.24 lakh. How many employees are there in that organization?

A. 400

B. 300

C. 200

D. 100

Ans: Option A

Explanation:

Required number of employees = (624000 – 600000)/60 = 24000/60 = 400

6. Find the value of [1-(1/3)][1-(1/4)][1-(1/5)]…..[1-(1/100)].

A. 2/54

B. 1/50

C. 5/49

D. 3/52

Ans: Option B

Explanation:

Given expression = (2/3)*(3/4)*(4/5) *….* (99/100) = 2/100 = 1/50.

7. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

A. Rs. 3500

B. Rs. 3750

C. Rs. 3840

D. Rs. 3900

Ans: Option D

Explanation:

Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.

Then, 10x = 4y   or   y = 5

15x + 2y = 4000

15x + 2 x (5x/2)=4000

20x=4000

X=200

So, y= (5x/2)

= (5x 200)/2

=500

Hence, the cost of 12 chairs and 3 tables = 12x + 3y

= Rs. (2400 + 1500)

= Rs. 3900.

8. (272 – 32)(124 + 176) / (17 * 15 – 15)

A. 0

B. 300

C. 2.25

D. None of these

Ans: Option B

Explanation:

No explanation

9. A man divides Rs.8600  among 5 sons, 4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?

A. 100

B. 500

C. 200

D. 600

Ans: Option C

Explanation:

Let the share of each nephews be Rs.x

Then, share of each daughter=Rs.4x

Share of each son=Rs.5x;

So, 5*5x+4*4x+2*x=8600

or, 25x+16x+2x=8600

or, 43x=8600

So, x = 200

10. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?

A. 63

B. 64.5

C. 62.5

D. 60.5

Ans: Option C

Explanation:

Let capacity of 1 bucket = x

Capacity of the tank = 25x

New capacity of the bucket = 2x/5

Hence, number of buckets needed = 25x/(2x/5) = 25×5/2 = 62.5

11. One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund?

A. Rs. 30,000

B. Rs. 50,000

C. Rs. 60,000

D. Rs. 90,000

Ans: Option C

Explanation:

Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 – x) respectively. Then,

(1/3)x=(1/2) (150000 – x)

(x/3) + (x/2)=75000

(5x/6)= 75000

X= (75000 x 6)/5= 90000

Savings in Public Provident Fund = Rs. (150000 – 90000) = Rs. 60000

12. Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?

A. 602

B. 528

C. 413

D. 512

Ans: Option D

Explanation:

Let number of children be n

If the number children = n, number of books each child will get = n/8

Total books distributed =n×n/8=n2/8

If the number children = n/2, number of books each child will get = 16

Total books distributed =n/2×16=8n

Since total books are same, we can write as n2/8 =8n

n/8=8

So, n=64

Total number of notebooks those were distributed = n2/8

= 64×64/8

= 64×8

= 512

13. What fraction of 35 needs to be added become 214?

A. 54

B. 234

C. 214

D. 34

Ans: Option B

Explanation:

Let x be the required fraction, 35x+35=21435x+35=94⇒35x=94−35=(45−12)20=3320⇒x=3320×53=114=234

14. 5005 – (5000/10)

A. 0.5

B. 5000

C. 50

D. 4505

Ans: Option D

Explanation:

No explanation

15. A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?

A. 3ft. 6 inches

B. 5ft. 9 inches

C. 8ft. 5 inches

D. 2ft. 7 inches

Ans: Option D

Explanation:

Length of board = 7ft. 9 inches

= (7*12+9) inches

= 93 inches

=>Length of each part = (93/3) inches

= 31 inches

= 2ft. 7 inches

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