Aptitude tricks for beginner and last minute revision

1. Train Problems 

Travelling towards each other
Relative speed= X+Y km/hr

Travelling in the same direction
Relative Speed= X-Y km/hr

2. Time and Work

• Work done by A and B 

            Work of A in one day =  LCM of X and Y

                                                               X

• X men in Y hours Z days:     

                                       

            Here, M= Men

            H= Hours
            D= Days
            W= Work

3. Boats Problem

• Let, Downstream speed = A km/hr

                 Upstream speed      = B km/hr

                        Speed of boat in still water = 1/2(A+B) km/hr
                        Speed of Stream = 1/2(A-B) km/hr

4. Percentage Problem

      Problem with phrases,

• a is what percent of b
• what percent of b is a
• what percent is a of b

          Use

5. Interest Problems

• Simple Interest problems

         Here, SI = Simple Interest

                   P = Principle Amount

                   R = Rate for interest

                   T = Time

• Compound Interest 

           This formula is difficult to solve so,

           For two successive years with rates r1 and r2,

            Use this formula repetitively for two successive years to find the required solution.

6. Ratio 

 If a:b and b:c are given.  What is a:b:c?

7. Encoding Decoding problems:

    Problems on words decoding. Draw numbering diagram of all letters to solve this type of problems

      Example : HEATER encoded as KBDGHO then COOLER encode as?

      Find difference by mapping letters in the world 

       Here the difference is of alternative 2 letters

       hence answer is

8. Power of numbers

    Finding any power of a number using the unit position of the number.

• For powers of numbers with last digit 5, 6, 0, 1 also ends with same digit.
• xxx5^y  = zzz5
• xxx6^y = zzz6
• xxx0^y = zzz0
• xxx1^y = zzz1 

          You can find out the correct option from multiple choices using these last digits.

• For powers of numbers with last digit 9 and 4

         Example: 9¹ = 9

                         9² = 81

         For 4:

• For powers of numbers with last digit 2

          Powers of this numbers have last digit in 2, 4, 8, 6. This series repeats again and again.

            Can solve this type of example by dividing exponent by 4 and taking remainder as exponent

            Example : 2232¹⁵

            here, 15/4 so the remainder is 3

            hence 2232¹⁵ = 23 = 8 (As last digit of solution) 

• For powers of numbers with last digit 3

          Powers of this numbers have last digit in 3, 9, 7, 1. This series repeats again and again.

           Can solve this type of example by dividing exponent by 4 and taking remainder as exponent.   

           Same as above for 2.

• For powers of numbers with last digit 7

         Powers of this numbers have last digit in 7, 9, 3, 1. This series repeats again and again.

          Can solve this type of example by dividing exponent by 4 and taking remainder as exponent.   

          Same as above for 2 and 3.

• For powers of numbers with last digit 8

          Powers of this numbers have last digit in 8, 4, 2, 6. This series repeats again and again.

           Can solve this type of example by dividing exponent by 4 and taking remainder as exponent.

           Same as above for 2, 3 and 7.