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a. Rs. 8600

b. Rs. 9000

c. Rs. 9050

d. Rs. 9300

**Answer:** b. Rs. 9000

**Explanation:**

Simple Interest = | PRT |

100 |

Rate of interest = R = 8% quarterly = | R | = | 8 | = 2% |

4 | 4 |

Amount after 2.5 years = Principal + Simple Interest

Amount = 7500 + | 7500 x 10 x 2 | = 7500 + 1500 = Rs. 9000 |

100 |

Tip:

For half yearly interest:- R = | R | and T= 2T |

2 |

For quarterly interest:- R = | R | and T= 4T |

4 |

For monthly interest:- R = | R | and T= 12T |

12 |

a. Rs. 4000

b. Rs. 4050.33

c. Rs. 4066.01

d. Rs. 4106.67

**Answer:** c. Rs. 4066.01

**Explanation:**

Down payment = Rs. 4000

Remaining Amount = Rs. 20000 - Rs. 4000 = Rs. 16000

After 4 months total amount to be paid = 16000 + Simple Interest on 16000

Simple Interest = | PRT | ; T = 4 months = | 4 | years |

100 | 12 |

∴ Total Amount = 16000 + | 16000 x 8 x 4 | = 16000 + 426.67 = Rs. 16426.67 |

12 x 100 |

Total installments = 4 (One installment per month)

Simple and Easy rule -

If there are 'n' installments, then, 1^{st} installment will have interest for (n-1) months, 2^{nd} will have interest for (n-2) months and so on.

So in this case, n=4

∴ 1

2

3

4

Let each installment be of Rs. A

Total Amount = 4 Installments + Interest on those 4 Installments

∴ Total Amount = 4A + | P x R x T |

100 |

P = A (same amount 'A' for all installments)

From above rule we can calculate effective time period 'T'

T (for interest calculation) = 3months + 2 months + 1 month + 0 months

∴ T = 6months = | 6 | years |

12 |

∴ Total Amount = 4A + | A x 8 x 6 | = 4A + | 4A | = | 101A |

100 x 12 | 100 | 25 |

∴ 16426.67= | 101A |

25 |

Tip:

Since rate of interest is same we can use above short cut.

If rate of interest or installment amount (A) or both varies then we have to calculate interest

Since rate of interest is same we can use above short cut.

If rate of interest or installment amount (A) or both varies then we have to calculate interest

separately for each installment by applying formula SI = | PRT | for every installment. |

100 |

a. 6.67%

b. 12.5%

c. 13.33%

d. 24%

**Answer:** c. 13.33%

**Explanation:**

Original amount = P

In T = 30 years, Amount = 5P

∴ Interest received in 30 years = 5P - P = 4P

Simple Interest = | PRT |

100 |

∴ 4P = | P x R x 30 |

100 |

a. 3 years

b. 5 years

c. 7 years

d. 7.5 years

**Answer:** d. 7.5 years

**Explanation:**

Let initial amount = P

In T = 15 years, Amount becomes 7P

So, Simple Interest = 7P - P = 6P = | P x R x 15 | ---------> As, SI = | PRT |

100 | 100 |

R = 40%; Amount = 10P.

So, Simple Interest = 10P - P = 9P = | P x 40 x T |

100 |

a. Rs. 1500 and 7 years

b. Rs. 1800 and 5.5 years

c. Rs. 1900 and 8.25 years

d. Rs. 2000 and 20 years

**Answer:** b. Rs. 1800 and 5.5 years

**Explanation:**

Let Simple Interest be S

Original sum 'P' and Time 'T' remains same

Also, 3% increase in rate of interested means, New rate = 15%

Increase of 300 Rs/- in the final amount means, New amount = Rs 3300/-

So, Amount 2 - Amount 1 = (P+S1) - (P+S2) = S1-S2

∴ 3300 - 3000 = S1-S2

∴ S1-S2 = 300

∴ | P x 15 x T | - | P x 12 x T | = 300 --------> As, Simple Interest = | PRT |

100 | 100 | 100 |

∴ | 3PT | = 300 |

100 |

For R = 15%,

Simple Interest = | P x 15 x T | = | 10000 x 15 | = Rs. 1500 |

100 | 100 |

Also, PT = 10000

∴ T = | 10000 | = 5.55 years (Time period) |

1800 |