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## Arithmetic: Simple Interest Test - 2

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Question 1 |

Maninder owes Prashant Rs. 1573, payable one and a half yr hence. Also Prashant owes Maninder Rs.1444.50, payable 6 months hence. If they want to settle the account forthwith, keeping 14% as the rate of interest, then who should pay whom and how much?

Maninder to Prashant, Rs. 28.50 | |

Maninder to Prashant, Rs. 50 | |

Prashant to Maninder, Rs. 37.50 | |

Prashant to Maninder, Rs. 50 |

Question 1 Explanation:

Let the present value of what Maninder owes Prashant be Rs v.

=> Then, v + {(v x 14 x 3) / (2 x 100)} = 1573

=> v+ (21/100) v =1573

=> 121v/100 = 1573

=> v= (1573 x 100)/121=Rs. 1300

Let u be the present value of what Prashant owes Maninder.

=> u +u x (1/2) x (14/100) = Rs 1444.50

=> u +(7/100u) = 1444.50

=> u= (1444.50 x100)/107 = Rs. 1350

Hence, Prashant owes Rs 50 to Maninder

=> Then, v + {(v x 14 x 3) / (2 x 100)} = 1573

=> v+ (21/100) v =1573

=> 121v/100 = 1573

=> v= (1573 x 100)/121=Rs. 1300

Let u be the present value of what Prashant owes Maninder.

=> u +u x (1/2) x (14/100) = Rs 1444.50

=> u +(7/100u) = 1444.50

=> u= (1444.50 x100)/107 = Rs. 1350

Hence, Prashant owes Rs 50 to Maninder

Question 2 |

A computer is available for Rs. 39000 cash or Rs. 17000 as cash down payment followed by five monthly instalments of Rs. 4800 each. What is the rate of interest per annum under the instalment plan?

35.71% | |

37.71% | |

36.71% | |

38.71% |

Question 2 Explanation:

Given statements are:

Cash price of computer, CP= Rs39000

Cash down payment, DP= Rs 17000

Balance due, after lst instalment, BD = Rs22000

P = value of instalment = Rs. 4800

n = no. of instalments = 5

R = rate of interest

=> (1+nR/1200) BD = [1+ {(n-1) R/2400}] nP

=> (1+5R/1200)22000 = [1+ {4R/2400}] x 5x 4800

=> (1+5R/1200)11 = (1+ 4R/2400) x 12

=> 11 + 55R/1200 = 12 + (24R/1200)

=> {55R/1200 – 24R/1200} = 1 =>(31R/1200) =1

=> R= 1200/31 = 38.71%

Cash price of computer, CP= Rs39000

Cash down payment, DP= Rs 17000

Balance due, after lst instalment, BD = Rs22000

P = value of instalment = Rs. 4800

n = no. of instalments = 5

R = rate of interest

=> (1+nR/1200) BD = [1+ {(n-1) R/2400}] nP

=> (1+5R/1200)22000 = [1+ {4R/2400}] x 5x 4800

=> (1+5R/1200)11 = (1+ 4R/2400) x 12

=> 11 + 55R/1200 = 12 + (24R/1200)

=> {55R/1200 – 24R/1200} = 1 =>(31R/1200) =1

=> R= 1200/31 = 38.71%

Question 3 |

Sumit lent some money to Mohit at 5% per annum simple interest. Mohit lent the entire amount to Birju on the same day at 8

^{1}/_{2}% per annum. In this transaction after a year, Mohit earned a profit of Rs. 350. Find the sum of money lent by Sumit to Mohit.Rs 10000 | |

Rs 9000 | |

Rs 10200 | |

None of these |

Question 3 Explanation:

Let a be the amount lent by Sumit at 5% rate

So therefore according to the question

8

17a/200 – 5a/100 = 350

7a/200 =3500

a = 10000

So therefore according to the question

8

^{1}/_{2}% of a- 5% of a = 35017a/200 – 5a/100 = 350

7a/200 =3500

a = 10000

Question 4 |

A scooter costs Rs. 25000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of the 3 yr?

Rs 12500 | |

Rs 10000 | |

Rs 12800 | |

Rs 12000 |

Question 4 Explanation:

Since the value is decreased every year by 80%

So the current cost of scooter is = 25000 x 80/100 x 80/100 x 80/100

=Rs 12800

So the current cost of scooter is = 25000 x 80/100 x 80/100 x 80/100

=Rs 12800

Question 5 |

Ravi gave Rs 1200 on loan. Some amount he gave at 4% per annum simple interest and remaining at 5% per annum simple interest. After two years, he got Rs110 as interest. Then, the amounts given at 4% and 5% per annum simple interest are, respectively?

Rs 500, Rs 700 | |

Rs 800, Rs 300 | |

Rs 400, Rs 800 | |

Rs 1100, Rs 1100 |

Question 5 Explanation:

Let the amount given at 4% per annum be Rs a

:. Amount given at 5% per annum = Rs (1200 - a)

=> {(a x 4 x 2)/100} + {(1200 - a) x 5 x 2}/100 = 110

=> {- 2a + 12000}/100 = 110

And =>(1200 – a) = 1200 – 500 = Rs 700

:. Amount given at 5% per annum = Rs (1200 - a)

=> {(a x 4 x 2)/100} + {(1200 - a) x 5 x 2}/100 = 110

=> {- 2a + 12000}/100 = 110

And =>(1200 – a) = 1200 – 500 = Rs 700

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