Mixture and allegation Quiz 1

Percentage of Brandy in the new mixture
= \frac{\frac{7}{10}\times 150+30}{150+30}
= \frac{105+30}{180} \times 100%
= 0.75 \times 100%
=75%

Total amount in the vessel = 100L
After removing 30% of mixture:
Remaining acid = 80 \times \frac{100-30}{100} = 56L [/latex]
Remaining aqua = 20 \times \frac{100-30}{100} = 14L [/latex]
Now 2 litres aqua has been added to the mixture.
Therefore,Remaining aqua = 14 + 2 = 16L
Again,after removing 25% mixture:
Remaining acid = 56 \times \frac{75}{100}
=42L
Remaining aqua = 16 \times \frac{75}{100}
=12L
Now 3 litres acid has been added to the mixture.
Therefore, Remaining acid = 42 + 3 = 45L
Required percentage= \frac{12}{12+45} \times 100
=21.05%

from the first ornament, gold \frac{2}{3} \ times 18 =12

From the second ornament gold \frac{5}{6} \ times 24 =20

Thus, total gold=32 gm.

Milk in A=4/7 of whole milk in B=2/5 of whole milk in mixture A and B =1/2 of the whole.

C.P of 1 unit of A C.P of 1 unit of B
Rs. 4/7 Rs. ⅖

Mean Price
Rs. ½

1/10 1/14

Let the C.P of unit quantity be Re.1

Required ratio= \frac{1}{10}: \frac{1}{14}

=14:10
=7:5

We have a 15 litre solution containing 40% of groundnut in the coconut oil.
=> Quantity of groundnut in the solution = \frac{15\times 40}{100}= 6
Now 5 litre of coconut oil is added to the solution.
=> Total quantity of the new solution = 15 + 5= 20
Percentage of groundnut in the new solution = 6\times \frac{100}{20} = \frac{600}{20}
= 30%

The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96
=> Cost = Rs.80 / kg.
Let the three varieties be A, B, and C costing Rs.65, Rs.70 and Rs.105 respectively.
The mean price falls between B and C.
Hence the following method should be used to find the ratio in which they should be mixed.
Mean : 80
A:C=4:5 B:C=2:5
The resultant ratio A : B : C :: 40 : 8 : 25.

CP = 40 \times 8.50 + 55 \times 8.75
= 340 + 481.25
= 821.25
Profit = 40%

SP= \frac{(100 +40) }{100} \times C.P

= 1.4 \times 821.2

Total quantity = 40 + 55 = 95 kg

SP per kg = \frac{(1.4 \times 821.25)}{95} = 12

In the mixture of 45 litre,

Milk= \frac{45}{4} \times 4 =36 ltr

Water= \frac{45}{5} \times 1 =45 ltr

New ratio,

= 9 + 3 : 36 + 4

= 12 : 40 = 3 : 10

The quantity of milk in the mixture

= 35 \times \frac{4}{7}
=20 ltrs.
The quantity of water in the mixture
= 35 – 20 = 15 litres
Now, let the quantity of water added to the mixture be x litres. Then water becomes 60% of the total quantity of mixture.
Therefore, Required % of water in mixture
\frac{\text{total quantity of water}}{\text{total quantity of mixture}} =60 %

\frac{15+x}{35+x}=\frac{3}{5}

75 + 5x = 105 + 3x

⇒ 2x = 30

Therefore, x = 15 litres.

Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice

Rs. 15 Rs. 20

Mean price
Rs. x

(20-x) (x-15)


Therefore, \frac{20-x}{x-15} = \frac{2}{3}

60 - 3x = 2x - 30
x=18

Video solution: