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## Arithmetic: Simple Interest Test -6

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Question 1 |

Sanjay borrowed a certain sum from Anil at a certain rate of simple interest for 2 yr. He lent this sum to Ram at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4200 as compound interest but paid Rs. 4000 only as simple interest, find the rate of interest.

15% | |

20% | |

35% | |

10% |

Question 1 Explanation:

Let Sanjay borrowed Rs a

Rate be r % with time = 2 yr

Therefore 4000= (a x r x 2)/100

r x a = 200000 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ... (i)

=> a {1 + r/100}

=> (ar

=> 20r + 4000 = 4200.................................... from (i)

=> r = 10%

Rate be r % with time = 2 yr

Therefore 4000= (a x r x 2)/100

r x a = 200000 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ... (i)

=> a {1 + r/100}

^{2}= a + 4200=> (ar

^{2}/ 10000) + (2ar/100) =4200=> 20r + 4000 = 4200.................................... from (i)

=> r = 10%

Question 2 |

Two equal sums of money were invested, one at 4% and the other at 4

^{1}/_{2. }At the end of 7 yr, the simple interest received from the latter exceeded that received from the former by Rs. 31.50. Each sum was?Rs 1000 | |

Rs 500 | |

Rs 750 | |

Rs 900 |

Question 2 Explanation:

Let each sum be Rs a, then

From the given condition

{(a x 4 Â½ x7)/100} - {(a x 4 x7)/100} = 31.50

=> 7a/100 x Â½ = 63/2

=> a = Rs 900

From the given condition

{(a x 4 Â½ x7)/100} - {(a x 4 x7)/100} = 31.50

=> 7a/100 x Â½ = 63/2

=> a = Rs 900

Question 3 |

If the difference between the simple and the compound interests on same principal amount at 20% for 3 yr is Rs. 48, then the principal amount must be?

Rs 650 | |

Rs 600 | |

Rs 375 | |

Rs 400 |

Question 3 Explanation:

Let the principle amount be Rs 100

Then Simple Interest will be = (100 x 20 x 3)/100 = Rs 60

And the compound interest on the money will be

= {100(1+ 20/100)

= 100 x (6/5)

So the difference between two of them will be

(364/5) â€“ 60 = 64/5

If he difference is 64/5 m then the principal is Rs. 100

And if the difference is Rs. 48

Then the principle is {(100 x 5)/64} x 48 = Rs. 375

Then Simple Interest will be = (100 x 20 x 3)/100 = Rs 60

And the compound interest on the money will be

= {100(1+ 20/100)

^{3}} â€“ 100= 100 x (6/5)

^{3}â€“ 100 =364/5So the difference between two of them will be

(364/5) â€“ 60 = 64/5

If he difference is 64/5 m then the principal is Rs. 100

And if the difference is Rs. 48

Then the principle is {(100 x 5)/64} x 48 = Rs. 375

Question 4 |

I derive an annual income of Rs. 688.25 from Rs. 10000 invested partly at 8% per annum and partly at 5% per annum simple interest. How much of my money is invested at 5%?

Rs. 3725 | |

Rs. 4225 | |

Rs. 4800 | |

Rs. 5000 |

Question 4 Explanation:

Let the money which is invested be m

And the rate at which it invested = 5% (given)

There from the question

{(m x 1 x 5)/100} + {(10000 â€“ m) x 1 x 8}/100 = 688.25

=> 5m â€“ 8m + 80000 = 68825

=> 3m = 11175

=> m= Rs. 3725

And the rate at which it invested = 5% (given)

There from the question

{(m x 1 x 5)/100} + {(10000 â€“ m) x 1 x 8}/100 = 688.25

=> 5m â€“ 8m + 80000 = 68825

=> 3m = 11175

=> m= Rs. 3725

Question 5 |

What equal annual installment will discharge a debt of Rs. 2985 due in 6 years at 10% simple interest?

349 | |

453 | |

398 | |

none |

Question 5 Explanation:

If each equal annual installment is Rs a, then

Amount of Rs a in 5 years + Amount of Rs a in 4 years + Amount of Rs a in 3 years + Amount of Rs a in 2 year + Amount of Rs a in 5 years = Rs 299250

Or [a + (a X 10 X 5/100)] + [a + (a X 10 X 4/100)] + [a + (a X 10 X 3/100)] + [a + (a X 10 X 2/100)]+ [a + (a X 10 X 1/100)] + a = 2985

150 a + 140 a + 130 a + 120 a + 110 a + 100 a = 2985 X 100

750 a = 2985 X 100

a = 2985 X 100/750 = Rs 398

Amount of Rs a in 5 years + Amount of Rs a in 4 years + Amount of Rs a in 3 years + Amount of Rs a in 2 year + Amount of Rs a in 5 years = Rs 299250

Or [a + (a X 10 X 5/100)] + [a + (a X 10 X 4/100)] + [a + (a X 10 X 3/100)] + [a + (a X 10 X 2/100)]+ [a + (a X 10 X 1/100)] + a = 2985

150 a + 140 a + 130 a + 120 a + 110 a + 100 a = 2985 X 100

750 a = 2985 X 100

a = 2985 X 100/750 = Rs 398

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