# Simple Interest Questions

**FACTS AND FORMULAE FOR SIMPLE INTEREST QUESTIONS**

**1. Principal:** The money borrowed or lent out for a certain period is called the **principal **or the **sum**.

**2. Interest:** Extra money paid for using other's money is called **interest**

**3. Simple Interest (S.I.) : **If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called **simple interest.**

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then,

(i) $S.I=\left(\frac{P\times T\times R}{100}\right)$

(ii) $P=\left(\frac{100\times S.I}{R\times T}\right);R=\left(\frac{100\times S.I}{P\times T}\right)andT=\left(\frac{100\times S.I}{P\times R}\right)$

A) Rate = 7% and Time = 7 years. | B) Rate = 8% and Time = 8 years. |

C) Rate = 6% and Time = 6 years. | D) Rate = 5% and Time = 5 years. |

Explanation:

Let sum = X. Then S.I = 16x/25

Let rate = R% and Time = R years.

Therefore, (x * R * R)/100 = 16x/25 => R = 40/5 = 8

Therefore, Rate = 8% and Time = 8 years.

A) 5:8 | B) 6:7 |

C) 16:15 | D) 17:18 |

Explanation:

let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then,

Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300

$\frac{x*5*3}{100}+\frac{\left(1500-x\right){\displaystyle *}{\displaystyle 8}{\displaystyle *}{\displaystyle 3}}{100}=300$

x=800

Required ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15

A) 1.5 | B) 2.5 |

C) 3.5 | D) 4.5 |

Explanation:

Let the time be 'n' years, Then

$800\times {\left(1+\frac{5}{100}\right)}^{2}n=926.10={\left(1+\frac{5}{100}\right)}^{2}n=\frac{9261}{8000}={\left(\frac{21}{20}\right)}^{2}n={\left(\frac{21}{10}\right)}^{3}$

n = 3/2 or n= 1$\frac{1}{2}$ Years

A) 66%% | B) 6.5% |

C) 7% | D) 7.5% |

A) Rs.35 | B) Rs.245 |

C) Rs.350 | D) cannot be determined |

Explanation:

We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.

A) 17.5 lakhs | B) 21 lakhs |

C) 15 lakhs | D) 20 lakhs |

Explanation:

Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 - x).

The elder daughter’s money earns interest for (21 - 16) = 5 years @ 10% p.a simple interest.

The younger daughter’s money earns interest for (21 - 8.5) = 12.5 years @ 10% p.a simple interest.

As the sum of money that each of the daughters get when they are 21 is the same,

$x+\frac{5*10*x}{100}=\left(3,500,000-x\right)+\frac{12.5*10*\left(3,500,000-x\right)}{100}$

$x+\frac{50}{x}=3,500,000-x+\frac{125}{100}*3,500,000-\frac{125x}{100}$

$2x+\frac{50x}{100}+\frac{125x}{100}=3,500,000*\left(1+\frac{5}{4}\right)$

$\frac{200x+50x+125x}{100}=\frac{9}{4}*\left(3,500,000\right)$

=>$x=2,100,000=21lakhs$

A) 3.46% | B) 4.5% |

C) 5% | D) 6% |

Explanation:

Let the original rate be R%. Then, new rate = (2R)%.

Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.1/3 year(s).

$\left(\frac{725*R*1}{100}\right)+\left(\frac{362.50*2R*1}{100*3}\right)=33.50$

=> (2175 + 725) R = 33.50 x 100 x 3

=> (2175 + 725) R = 10050

=> (2900)R = 10050

=> $R=\frac{10050}{2900}=3.46$

Original rate = 3.46%

A) Rs.350 | B) Rs.450 |

C) Rs.550 | D) Rs.650 |

Explanation:

P = Rs. 6250, R = 14 % & T = (146/365) years = 2/5 years .

S.I=$Rs.\left[\raisebox{1ex}{$6250*14*{\displaystyle \frac{2}{5}}$}\!\left/ \!\raisebox{-1ex}{$100$}\right.\right]=Rs.350$