# 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| =

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

Q:

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :

 A) 35 B) 38 C) 40 D) 42

Explanation:

Let the number of correct answers be X.

Number of incorrect answers = (60 – X).

4x – (60 – x) = 130

=> 5x = 190

=> x = 38

199 67523
Q:

If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?

 A) 500 B) 1000 C) 1500 D) 2000

Explanation:

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

Then, 2x + 3y = 3500 ...(i)

and 3x + 2y = 4000 .....(ii)

solving (i) and (ii) we get x = 1000, y = 500

76 28687
Q:

A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :

 A) 30 birds B) 60 birds C) 72 birds D) 90 birds

Explanation:

Let the no of shots be x. Then,

Shots fired by A =(5/8)x

Shots fired by B = (3/8)x

Killing shots by A = 1/3 of (5/8)x  = (5/24)x

Shots missed by B = 1/2 of (3/8)x = (3/16)x

(3/16)x = 27 $⇒$ x =144

Birds killed by A = (5/24)x = (5/24)*144 = 30

70 24939
Q:

If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3  is equal to :

 A) 22 B) 23 C) 24 D) 25

Explanation:

3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)

= (6 + 10 - 9 + 15) = 22.

54 18131
Q:

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

 A) 160 B) 175 C) 180 D) 195

Explanation:

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

Therefore,  160 * 2.40 + x * 3.20 = 432

=> 3.20x = 432 - 384 = 48

=> x = 15.

Hence, total hours of work = (160 + 15) = 175.

21 17261
Q:

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 bucket is reduced to two-fifth of its present ?

 A) 52.5 B) 62.5 C) 72.5 D) 82.5

Explanation:

Let the capacity of 1 bucket = x.

Then, capacity of tank = 25x.

New capacity of bucket  = (2/5)x

$\inline \therefore$Required no of buckets = 25x/(2x/5)  = 62.5

24 16568
Q:

If a + b + c = 13, $a2+b2+c2=69$ then find the ab + bc + ca :

 A) 10 B) 30 C) 50 D) 70

Explanation:

$a+b+c2=a2+b2+c2+2ab+bc+ca$

$2ab+bc+ca=a+b+c2-a2+b2+c2=169-69=100=ab+bc+ca=50$

35 15297
Q:

A tank is 2/5 full. If 16 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:

 A) 28 litres B) 32 litres C) 35 litres D) 42 litres