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# Mixture and Alligation #28

 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

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

Arka Das
2015-04-04 10:45:32
how 2/7 is being derived
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)
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