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# Solved Examples(Set 6) - Mixture and Alligation

 26. A trader has 1600 kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole , find the quantity sold at 12%. A. 800 kg B. 1600 kg C. 1200 kg D. 1400 kg

Explanation:

By rule of alligation,

 % Profit by selling part1 % Profit by selling part2 8 12 Net % Profit 11 12 - 11 = 1 11 - 8 = 3

=> Quantity of part1 : Quantity of part2 = 1 : 3

Given that total quantity = 1600 kg

Hence, quantity of part2 (quantity sold at 12% profit)
$=1600 × \dfrac{3}{4} = 1200$

 27. In 40 litres of a mixture, the ratio of milk to water is 7:1. In order to make the ratio of milk to water as 3:1, the quantity of water that should be added to the mixture will be A. $6\text{ litre}$ B. $5 \dfrac{2}{3}\text{ litre}$ C. $6 \dfrac{2}{3}\text{ litre}$ D. $4 \dfrac{1}{3}\text{ litre}$

Explanation:

By rule of alligation,

 Concentration of waterin pure water : 1 Concentration of waterin mixture : $\dfrac{1}{8}$ Concentration of water inthe final mixture : $\dfrac{1}{4}$ $\dfrac{1}{4}-\dfrac{1}{8}=\dfrac{1}{8}$ $1-\dfrac{1}{4}=\dfrac{3}{4}$

Quantity of water : Quantity of mixture $=\dfrac{1}{8}:\dfrac{3}{4}=1:6$

Given that quantity of mixture = 40 litre
=>Quantity of water : 40 = 1 : 6
=> Quantity of water $=40 × \dfrac{1}{6} = 6\dfrac{2}{3}$ litre

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

 29. In 1 kg mixture of iron and manganese, 20% is manganese. How much iron should be added so that the proportion of manganese becomes 10% A. 2 kg B. 1 kg C. .5 kg D. 1.5 kg

Explanation:

By rule of alligation,

 Percentage concentration ofmanganese in the mixture : 20 Percentage concentration ofmanganese in pure iron : 0 Percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10

=> Quantity of the mixture : Quantity of iron = 10 : 10 = 1 : 1

Given that quantity of the mixture = 1 kg

Hence quantity of iron to be added = 1 kg

 30. John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit at the cost price? A. Rs.8 B. Rs.16 C. Rs.20 D. Rs.12

Explanation:

CP $=20×8.5+35×8.75$
$=170+306.25=476.25$

Profit = 40%

$\text{SP }=\dfrac{(100+\text{Profit%})}{100}×\text{ CP}\\= \dfrac{(100+40)}{100}× 476.25 \\= \dfrac{140}{100}× 476.25 \\\\= \dfrac{140}{4}× 19.05 = 35 × 19.05$

Total quantity = 20 + 35 = 55 kg

SP per kg $=\dfrac{35 × 19.05}{55} = \dfrac{7 × 19.05}{11}$
$\approx \dfrac{7 × 19}{11} \approx \dfrac{133}{11} \approx 12$