First and foremost the most important trick is to solve using options

### 1. QUADRATIC TRICK

Ax²+Bx+C=0Split the middle terms (B) and product terms (AC) mentally.

**For example:**187 x²+6x-1=0 …………..quadratic equation

-187=17 x -11 after getting the prime factors 17 and 11 I realized 17-11=6

factors 17 and -11

reverse signs -17 and 11

divide by A: -17/187 and 11/187 so the factors are x = -1/11 and 1/17 153y²-26y+1=0

+153= 3 x 3 x 17 to get -26 the factors can be arranged as -9-17=-26 and -9 x -17=+153 factors -9 and -17

reverse signs 9 and 17

divide by A: 9/153 and 17/153 factors are: y =1/17 and 1/9

y>=x.

### 2. Profit , loss and discount

Profit and Loss questions can be simply treated as ration questionsIf said 20 perc discount = 20/100

So bring it in SP: CP terms i.e. 80:100 SP is 80 CP is 100 SP-CP= 80-100=20 (discount)

Similarly marked up by 5perc is 5/100 but since it’s marked up it becomes 105:100 i.e. SP = 105

CP= 100 .SP-CP=105-100.

A shopkeeper marks up his goods by 20% and gives a discount of 5%.Also he uses a false balance which reads 1000gms for 750gms .What is his total profit percentage.

Mark up of 20% is 120/100

Discount by 5% is 95 /100

Claimed weight /actual weight 1000/750 (analyze if situation of profit num>den

If situation of loss num<den)

Profit percent: 13/25 x 100=52%

A mixture contains wine and water in the ratio 3:2 and another contains them in the ratio 4:3.If they are mixed in the ratio 2:3, what is the ratio of wine and water in the resultant mixture?

### 3. Ratio and proportion

The trick is in taking it as a unitA mixture contains wine and water in the ratio 3:2 and another contains them in the ratio 4:3.If they are mixed in the ratio 2:3, what is the ratio of wine and water in the resultant mixture?

wine | water | unit | |
---|---|---|---|

1^{st} mixture |
3 x7 | 2 x7 | 5 x7 |

2^{nd} mixture |
4 x5 | 3 x5 | 7 x5 |

- Make the units equal.
- Multiply the final equal table with the ratio in which they are mixed (2:3).

wine | Water | unit |
---|---|---|

21 | 14 | 35 |

20 | 15 | 35 |

Wine | Water | Unit |
---|---|---|

42 | 28 | 70 |

60 | 45 | 105 |

102 | 73 |

### 4. Compound Interest

Rather than calculating compound interest using formula just use percentage method. The simple interest accrued on an amount of Rs 17000 at the end of four years is Rs 6800.What would be the compound interest accrued on the same amount at the same rate in the same period

**Interest accrued:**1700+1870+2057+2262.7 = 7889.7

### 5. Simplification – Digit sum

Firstly add all the digits of a number to bring a single no.Rule if sum is 9 strike it off and write 0

Any other no. is considered

Secondly try and find the units digit which will further make the answer a 100 perc sure.

###
__Example :__

__Example :__

#### Ques 1.

….. 123 x 456 x 781a)43804728

b) 53804728

c)53804528

d) 33804958

__Ans.__So digit sum is zero and unit’s digit is 8

Which ever option has digit sum as zero is the ans

4+3+8+0+4+7+2+8 = 36 (9=0)

5+3+8+0+4+7+2+8 = 37 (10=1)

5+3+8+0+4+5+2+8 = 35 (8)

3+3+8+0+4+9+5+8 = 40 (4)

#### Ques 2

6269+0.75 x 4444+0.8 x 185a)9759

b)9750

c)9740

d)9755

e)9655

**Ans:**

= 6269+3333+4 x 37

Digit sum : 5+3+4 x 1 = 5+3+4 = 3

Unit’s digit :0

9+7+5+9 = 3

9+7+5+0 = 3

9+7+4+0 = 2

9+7+5+5 = 0

9+6+5+5 = 7

Ans is clearly b where digit sum is 3 and units digit is 0.