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28. Some amount out of Rs.7000 was lent at 6% per annum and the remaining was lent at 4% per annum. If the total simple interest from both the fractions in 5 years was Rs.1600, the sum lent at 6% per annum was | |

A. Rs. 2000 | B. Rs. 2400 |

C. Rs. 1800 | D. Rs. 2200 |

Answer: Option A

Explanation:

Total simple interest received , I = Rs.1600

Principal , p = 7000

period, n = 5 years

Rate of interest, r = ?

Simple Interest, $I=\dfrac{pnr}{100}$

$\Rightarrow 1600 = \dfrac{7000 × 5 × r}{100}\\\Rightarrow r = \dfrac{1600 × 100}{7000 × 5} = \dfrac{160}{35} = \dfrac{32}{7}\%$

By rule of alligation,

Rate of interest % from part1 | Rate of interest % from part2 | |||||||||

6 | 4 | |||||||||

Net rate of interest % | ||||||||||

$\dfrac{32}{7}$ | ||||||||||

$\dfrac{32}{7}-4=\dfrac{4}{7}$ | $6-\dfrac{32}{7}=\dfrac{10}{7}$ |

=> Part1 : part2 $=\dfrac{4}{7}:\dfrac{10}{7}=4:10=2:5$

Given that total amount is Rs.7000. Therefore, the amount lent at 6% per annum (part1 amount)

$=7000 × \dfrac{2}{7} = \text{Rs. }2000$

Dev

2015-04-08 19:05:10

Part1 : part2 = 2 : 5

part1+part2 = 7000

Sp part1 = 7000*2/(2+5)

and part2 = 7000*5/(2+5)

part1+part2 = 7000

Sp part1 = 7000*2/(2+5)

and part2 = 7000*5/(2+5)

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