# Aptitude - Simplification

- Simplification - Formulas
- Simplification - General Questions

Let number of notes of each denomination be *x*.

Then *x* + 5*x* + 10*x* = 480

16*x* = 480

*x* = 30.

Hence, total number of notes = 3*x* = 90.

Let the number of students in rooms A and B be *x* and *y* respectively.

Then, *x* - 10 = *y* + 10 *x* - *y* = 20 .... (i)

and *x* + 20 = 2(*y* - 20) *x* - 2*y* = -60 .... (ii)

Solving (i) and (ii) we get: *x* = 100 , *y* = 80.

The required answer A = 100.

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

Then, 10x = 4y or y = |
5 | x. |

2 |

15*x* + 2*y* = 4000

15x + 2 x |
5 | x = 4000 |

2 |

20*x* = 4000

*x* = 200.

So, y = |
5 | x 200 | = 500. | ||

2 |

Hence, the cost of 12 chairs and 3 tables = 12*x* + 3*y*

= Rs. (2400 + 1500)

= Rs. 3900.

*a*-

*b*= 3 and

*a*

^{2}+

*b*

^{2}= 29, find the value of

*ab.*

2*ab* = (*a*^{2} + *b*^{2}) - (*a* - *b*)^{2}

= 29 - 9 = 20

*ab* = 10.

Let the price of a saree and a shirt be Rs. *x* and Rs. *y* respectively.

Then, 2*x* + 4*y* = 1600 .... (i)

and *x* + 6*y* = 1600 .... (ii)

Divide equation (i) by 2, we get the below equation. => x + 2y = 800. --- (iii) Now subtract (iii) from (ii) x + 6y = 1600 (-) x + 2y = 800 ---------------- 4y = 800 ---------------- Therefore, y = 200. Now apply value of y in (iii) => x + 2 x 200 = 800 => x + 400 = 800 Therefore x = 400

Solving (i) and (ii) we get *x* = 400, *y* = 200.

Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.