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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 kgB. 1600 kg
C. 1200 kgD. 1400 kg
Discuss
answer with explanation

Answer: Option C

Explanation:

By rule of alligation,

% Profit by selling part1% Profit by selling part2
812
Net % Profit
11
12 - 11 = 111 - 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. $4 \dfrac{1}{3}\text{ litre}$
Discuss
answer with explanation

Answer: Option C

Explanation:

By rule of alligation,

Concentration of water
in pure water : 1
Concentration of water
in mixture : $\dfrac{1}{8}$

Concentration of water in
the 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. 2000B. Rs. 2400
C. Rs. 1800D. Rs. 2200
Discuss
answer with explanation

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 part1Rate of interest % from part2
64
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 kgB. 1 kg
C. .5 kgD. 1.5 kg
Discuss
answer with explanation

Answer: Option B

Explanation:

By rule of alligation,

Percentage concentration of
manganese in the mixture : 20
Percentage concentration of
manganese in pure iron : 0
Percentage concentration of manganese in the final mixture
10
10 - 0 = 1020 - 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.8B. Rs.16
C. Rs.20D. Rs.12
Discuss
answer with explanation

Answer: Option D

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

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