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## Arithmetic: Simple Interest Test -1

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Question 1 |

If Rs. 1000 be invested at interest rate of 5% and the interest be added to the principal after 10 yr, then the number of years in which it will amount to Rs 2000 is ?

16 ^{2}/_{3} yr | |

16 ^{1}/_{4} yr | |

16 yr | |

11 yrr |

Question 1 Explanation:

First we calculate the SI for 10 years

SI for 10 years is

=> (1000 x 5 x 10)/100 = Rs 500

Now new principal is

P = Rs. 1500

A = Rs. 2000

SI = Rs. 500

SI = (P x R xT)/100

T = (500 x 100)/ 1500 x 5 = 16

So, the total amount of Time is 10 +6

SI for 10 years is

=> (1000 x 5 x 10)/100 = Rs 500

Now new principal is

P = Rs. 1500

A = Rs. 2000

SI = Rs. 500

SI = (P x R xT)/100

T = (500 x 100)/ 1500 x 5 = 16

^{2}/_{3}yrSo, the total amount of Time is 10 +6

^{2}/_{3}yr = 16^{2}/_{3}yQuestion 2 |

A sum of Rs7700 is to be divided among three brothers Bharat, Rakshit and Maninder in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 yr respectively remains equal. The share of Bharat is more than that of Maninder by:

Rs 2800 | |

Rs2500 | |

Rs3000 | |

Rs2700 |

Question 2 Explanation:

Let the three of them get p, q, r amount respectively

So at the rate of 5%, they have

(p x 5 x1 )/100 =(q x 5 x2 )/100 =(r x 5 x3)/100

=>p = 2q =3r

=> p:q:r = 6 : 3: 2

So the required amount = {(6 -2)/(6+3+2)} x 7700 = Rs 2800

So at the rate of 5%, they have

(p x 5 x1 )/100 =(q x 5 x2 )/100 =(r x 5 x3)/100

=>p = 2q =3r

=> p:q:r = 6 : 3: 2

So the required amount = {(6 -2)/(6+3+2)} x 7700 = Rs 2800

Question 3 |

Amit borrowed a certain sum of money for 2 yr at 8% per annum on simple interest and immediately lent it to Ravi but at compound interest and gained Rs 16. What amount did Amit borrow?

Rs1600 | |

Rs2500 | |

Rs24000 | |

Rs1800 |

Question 3 Explanation:

Let the amount borrowed by Amit is A

Then, A [(1+8/100)

=> 0.1664A - 0.16A = 16

=> A = (16/0.0064) = Rs. 2500.

Then, A [(1+8/100)

^{2}- 1] – (A x 8x2)/100 =16=> 0.1664A - 0.16A = 16

=> A = (16/0.0064) = Rs. 2500.

Question 4 |

Anu owes Biresh Rs. 1120 payable 2 yr hence; Biresh owes Anu Rs.1081.50 payable 6 months. If they decide to settle their accounts forthwith by making the payments of money due right now, and the rate of interest be 6% per annum, then who should pay and how much?

Anu, Rs70 | |

Biresh, Rs 50 | |

Anu, Rs50 | |

Biresh, Rs 70 |

Question 4 Explanation:

Let the present amount for Anu be= A

= (1120 – A) = (A x 6 x 2)/100

=> A = 1000 (amount Anu owes to Biresh)

Let the present amount for Biresh be = B

=>1081.50 – B = (B x 6 x 1)/ (2 x100)

=> 108150 –100B = 3

=> B = Rs 1050 (Amount Biresh owes to Anu)

Therefore Biresh should pay Rs 50 to Anu

= (1120 – A) = (A x 6 x 2)/100

=> A = 1000 (amount Anu owes to Biresh)

Let the present amount for Biresh be = B

=>1081.50 – B = (B x 6 x 1)/ (2 x100)

=> 108150 –100B = 3

=> B = Rs 1050 (Amount Biresh owes to Anu)

Therefore Biresh should pay Rs 50 to Anu

Question 5 |

Natasha invested a certain sum of money in a simple interest bond whose value grew to Rs.300 at the end of 3 yr and to Rs.400 at the end of another 5 yr. What was the rate of interest in which he invested his sum?

12% | |

12.5% | |

6.67% | |

8.33% |

Question 5 Explanation:

Let principle = P

Let rate of interest =R

Then,

(P x R x 3)/100 + P = 300........................................1

(P x R x 8)/100 + P = 400.........................................2

Subtracting eq. 1 from eq.2 we get

(P x R x 5)/100 = 100

P x R = 2000

Now from eq. 1

(2000 x 3)/100 + P = 300

=> P = 240

Therefore 240 x R = 2000

R = 8.33%

Let rate of interest =R

Then,

(P x R x 3)/100 + P = 300........................................1

(P x R x 8)/100 + P = 400.........................................2

Subtracting eq. 1 from eq.2 we get

(P x R x 5)/100 = 100

P x R = 2000

Now from eq. 1

(2000 x 3)/100 + P = 300

=> P = 240

Therefore 240 x R = 2000

R = 8.33%

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