1. How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest? | |

A. 2 years | B. 3 years |

C. 1 year | D. 4 years |

| Discuss |

Here is the answer and explanation

Answer : Option A

Explanation :

P = Rs.900

SI = Rs.81

T = ?

R = 4.5%

$MF#%\text{T= }\dfrac{100 ×\text{SI}}{\text{PR}} = \dfrac{100 × 81}{900 × 4.5} = 2 \text{ years}$MF#%

2. Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If he paid Rs.686 as interest at the end of the loan period, what was the rate of interest? | |

A. 8% | B. 6% |

C. 4% | D. 7% |

| Discuss |

Here is the answer and explanation

Answer : Option D

Explanation :

Let rate = R%

Then, Time, T = R years

P = Rs.1400

SI = Rs.686

$MF#%\begin{align}&\text{SI= }\dfrac{\text{PRT}}{100} \\ \\

&\Rightarrow \text{686 = }\dfrac{\text{1400 × R × R}}{100} \\ \\

&\Rightarrow 686 = 14 \text{ R}^2 \\ \\

&\Rightarrow 49 = \text{R}^2 \\ \\

&\Rightarrow \text{R} = 7\end{align}$MF#%

i.e.,Rate of Interest was 7%

3. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is : | |

A. Rs. 700 | B. Rs. 690 |

C. Rs. 650 | D. Rs. 698 |

| Discuss |

Here is the answer and explanation

Answer : Option D

Explanation :

Simple Interest (SI) for 1 year = 854-815 = 39

Simple Interest (SI) for 3 years = 39 × 3 = 117

Principal = 815 - 117 = Rs.698

4. A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.c.p.a. in 5 years. What is the sum? | |

A. Rs. 2323 | B. Rs. 1223 |

C. Rs. 2563 | D. Rs. 2353 |

| Discuss |

Here is the answer and explanation

Answer : Option A

Explanation :

SI = Rs.929.20

P = ?

T = 5 years

R = 8%

$MF#%\text{P = }\dfrac{100 \times \text{SI}}{\text{RT}}=\dfrac{100 \times 929.20}{8 \times 5}\text{ = Rs.2323}$MF#%

5. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B? | |

A. Rs. 6400 | B. Rs. 7200 |

C. Rs. 6500 | D. Rs. 7500 |

| Discuss |

Here is the answer and explanation

Answer : Option A

Explanation :

Let the investment in scheme A be Rs.x

and the investment in scheme B be Rs.(13900 - x)

$MF#%\begin{align}&\text{We know that }\text{SI = }\dfrac{\text{PRT}}{100}\\\\
&\text{Simple Interest for Rs.x in 2 years at 14% p.a. = }\dfrac{x \times 14 \times 2}{100} = \dfrac{28x}{100}\\\\
&\text{Simple Interest for Rs.(13900 - x) in 2 years at 11% p.a. = }\dfrac{(13900 - x) \times 11 \times 2}{100} = \dfrac{22(13900 - x)}{100}\\\\
&\text{Total interest = Rs.3508}\\\\
&\dfrac{28x}{100} + \dfrac{22(13900 - x)}{100} = 3508\\\\
&28x + 305800 -22x = 350800\\\\
&6x = 45000\\\\
&x = \dfrac{45000}{6} = 7500\end{align}$MF#%

Investment in scheme B = 13900 - 7500 = Rs.6400

PRT/100 = 650

P * 10 * 1/100 = 650

P = 6500

The sum is Rs.6500

in 2 yrs the amount 1008 -

___________________________

the 1.5 yrs interest is 156

the 1 yr interest is 156/1.5 =104

the 2 yrs interest is 208 rs

principal=1008-208= 800

rate of interest=(104/800)*100

=13%

Simple Interest on P for 2 years = (1008-P)

P * 2 * R/100 = (1008-P)

2PR = 100(1008-P) ----(eq:1)

Simple Interest on P for 3.5 years = (1164-P)

P * 3.5 * R/100 = (1008-P)

3.5PR = 100(1164-P) ----(eq:2)

(eq:1)/(eq:2) 2/3.5 = 100(1008-P)/100(1164-P)

20/35 = (1008-P)/(1164-P)

4/7 = (1008-P)/(1164-P)

4(1164-P) = 7(1008-P)

4656 - 4P = 7056 - 7P

3P = 2400

P = 800

From eq1, 2*800*R = 100(1008-800)

2*800*R = 100*208

R = 13

Rate of Interest is 13%

B-12 LCM:48 - 4

A+B 2 days - 7

48/7 = 6

balance: 48-42 = 6

A- 3 (13th day)

B- 3, (3/4 day)

Ans: 13 3/4 days.

In day 1, only A works and total work gets completed = 1/16

In day 2, only B works and total work gets completed = 1/12

this pattern continues till total work gets completed

Work completed in every 2 days = 1/16 + 1/12 = 7/48

So in 2*6 = 12 days, 6*7/48 = 42/48 = 7/8 work gets completed

in 13th day, total work gets completed = 7/8 + 1/16 = 15/16

Remaining work = 1/16

days taken by B to complete this = (1/16)/(1/12) = 3/4 days

So total work gets completed in 13

^{3}/

_{4}days

A 3W |
B 4W |
A 3W |
B 4W |
A 3W |
B 4W |
A 3W |
B 4W |
A 3W |
B 4W |
A 3W |
B 4W |
A 3W |
B 3W |

Pls explain

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