Simplification Questions

FACTS  AND  FORMULAE  FOR  SIMPLIFICATION  QUESTIONS

 

 

1. BODMAS Rule: This rule depicts the correct sequence in which the operations are to be executed,so as to find out the value of a given expression. Here, 'B' stands for bracket , 'O' for of , 'D' for division and 'M' for multiplication, 'A' for addition and 'S' for subtraction.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order(), {} and [].

After removing the brackets, we must use the following operations strictly in the order:

(1) of    (2)division   (3) multiplication   (4)addition   (5)subtraction.

 Modulus of a real number : Modulus of a real number a is defined as |a| = aif a>0-aif a<0

 

2. Virnaculum (or bar) : When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.

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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12 7449
Q:

Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees

A) 8 B) 9
C) 10 D) 11
 
Answer & Explanation Answer: B) 9

Explanation:

26 trees have 25 gaps between them,
Required distance (225/25) = 9

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6 7356
Q:

Given that 100.48 = x,  100.70 = y and xz = y2,  then the value of z is close to ___ ?

A) 3.7 B) 2.7
C) 3.6 D) 2.9
 
Answer & Explanation Answer: D) 2.9

Explanation:

xz = y2        10(0.48z) = 10(2 x 0.70) = 101.40

 0.48z = 1.40

 z = 140/18 = 35/12 = 2.9 (approx.)

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10 7146
Q:

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

A) 23 B) 24
C) 25 D) 26
 
Answer & Explanation Answer: D) 26

Explanation:

Let, Hema attempted 'k' sum correctly, then

k x 3 -2 x(35-k) = 60
5k = 130
k = 26

so 26 correct sums.

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9 6942
Q:

A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is 

A) 42 B) 45
C) 38 D) 36
 
Answer & Explanation Answer: B) 45

Explanation:

Let number of 20 ps coins = x and

number of 25 ps coins = y

Given total coins in the bag = 50

x + y = 50.......(1)

But the total money in the bag = Rs. 10.25

0.20x + 0.25y = 10.25

20x + 25y = 1025.........(2)

Now multiplying (1) by 25 we get

25x+25y=1250.............(3)

By solving (2) and (3)

20x + 25y = 1025;

=> x = 45;

Then, the no. of 20 ps coins are 45.

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5 6425
Q:

A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?

A) 300 B) 150
C) 175 D) 200
 
Answer & Explanation Answer: B) 150

Explanation:

Half of the cloth = 37.5/2
From 1 meter he will make 8 pieces
=> in 37.5/2 ---- ?

37.5/2 x 8

= 150.

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5 6023
Q:

23x12+49x15312+50 = ?

A) 0.5 B) 1
C) 2 D) 3
 
Answer & Explanation Answer: B) 1

Explanation:

276+35961+50 = 10111011 = 1

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2 5972
Q:

Simplyfiy : 314÷114-12212-14+16

A) 78 B) 88
C) 98 D) 108
 
Answer & Explanation Answer: A) 78

Explanation:

Given exp =134÷54-1252-3-212134÷54-1252-112

 

134÷54-1230-112 = 134÷54-2924

 

 = 134÷30-2924=78

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