# 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| = $\left\{\begin{array}{ll}a& ifa0\\ -a& ifa0\end{array}\right.$

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

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

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

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 $\Rightarrow $ *x* =144

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

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.

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

=> 3.20*x* = 432 - 384 = 48

=> *x* = 15.

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

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

Required no of buckets = 25x/(2x/5) = 62.5

A) 10 | B) 30 |

C) 50 | D) 70 |

Explanation:

${\left(a+b+c\right)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2\left(ab+bc+ca\right)$

$2\left(ab+bc+ca\right)={\left(a+b+c\right)}^{2}-\left({a}^{2}+{b}^{2}+{c}^{2}\right)\phantom{\rule{0ex}{0ex}}=169-69=100\phantom{\rule{0ex}{0ex}}=\left(ab+bc+ca\right)=50$

A) 28 litres | B) 32 litres |

C) 35 litres | D) 42 litres |

Explanation:

Let the capacity of the tank be x litres.

Then, (6x/7 - 2x/5) = 16 <=> 30x - 14x = 16*35 <=> x = 35