a. Rs. 635.20, 12.50%

b. Rs. 656.10, 11.11%

c. Rs. 696.50, 12.50%

d. Rs. 698.80, 11.11%

**Answer:** b. Rs. 656.10, 11.11%

**Explanation:**

If Raj allows, one more year, time period becomes 4 years.

4 years - 3 years = 1 year

Thus, we can say that Rs. 900 becomes Rs. 1000 in 1 year.

∴ Interest = Rs. 1000 - Rs. 900 = Rs. 100

For 1 year time period, Simple Interest = Compound Interest

∴ | P x R x T | = | 900 x R x 1 | = Rs. 100 |

100 | 100 |

∴ R = | 100 | % = 11.11% |

9 |

Also, in 3 years by compound interest the original sum becomes Rs. 900 at the rate 11.11% or | 100 | %. |

9 |

∴ Amount = Rs. 900 = P | 1 + | R | n | ||

100 |

∴ 900 = P | 1 + | 100 | 3 | ||

9 x 100 |

a. Rs. 454.50

b. Rs. 464

c. Rs. 464.10

d. Rs. 480.60

**Answer:** c. Rs. 464.10

**Explanation:**

Simple Interest = | P x R x T | = Rs. 400 |

100 |

∴ | P x 10 x 4 | = 400 |

100 |

For Compound Interest, Amount = P | 1 + | R | n | ||

100 |

∴ Amount = 1000 | 1 + | 10 | 4 | ||

100 |

a. 75,550

b. 77,250

c. 79,860

d. 80,500

**Answer:** c. 79,860

**Explanation:**

Tip:

P= Population; R = Rate of increase or decrease; n= number of years;

'+' = during increase; '-'= during decrease

Population after n years = P | 1 ± | R | n | ||

100 |

'+' = during increase; '-'= during decrease

Population after 3 years = 60,000 | 1 + | 10 | 3 | ||

100 |

= | 60,000 x 11 x 11 x 11 | = 79,860 |

10 x 10 x 10 |

a. Rs. 11000

b. Rs. 12800

c. Rs. 14400

d. Rs. 16400

**Answer:** c. Rs. 14400

**Explanation:**

Tip:

In cases where rate of interest is given and the number of installments = 2, then you should use the following trick to solve such problems quickly.

**(1 ^{st} fraction x 2^{nd} fraction) x Installment = Sum**

First express the rate of interest as a fraction.

∴ R = 20% = | 20 | = | 1 |

100 | 5 |

Next, derive first fraction as = | Denominator | = | 5 | = | 5 |

Numerator+Denominator | 1+5 | 6 |

Using this fraction, derive 2^{nd} fraction as = | Numerator+Denominator | = | 5+6 | = | 11 |

Denominator | 6 | 6 |

∴ | 5 | x | 11 | x Installment = Sum | ||

6 | 6 |

Installment is the value of each installment (including interest on the installment)

∴ | 5 | x | 11 | x Installment = 22000 | ||

6 | 6 |

a. Rs. 1220

b. Rs. 10000

c. Rs. 11250

d. Rs. 13500

**Answer:** c. Rs. 11250