Mixture Problems MCQ Quiz - Objective Question with Answer for Mixture Problems - Download Free PDF

Given:

Cost of first variety (C₁) = ₹200 per kg

Cost of second variety (C₂) = ₹300 per kg

Blending ratio = 5 : 4

Selling Price (SP) = ₹250 per kg

Formula used:

Cost Price (CP) of blended tea = \(\frac{C_1 \times W_1 + C_2 \times W_2}{W_1 + W_2}\)

Profit/Loss % = \(\frac{SP - CP}{CP} \times 100\)

Calculation:

CP = (200 × 5 + 300 × 4) / (5 + 4)

CP = (1000 + 1200) / 9 = 2200 / 9 ≈ ₹244.44 per kg

Profit % = ((250 − 244.44) / 244.44) × 100

= (5.56 / 244.44) × 100 ≈ 2.27% (Profit)

∴ The correct answer is option (2): Profit of 2.27%

Given:

Total quantity = 320 kg

Cost price per kg = ₹115

80% of 320 kg = 256 kg sold at ₹160/kg

Remaining = 320 - 256 = 64 kg

Overall profit required = 60%

Formula Used:

Total cost price = Quantity × Cost per kg

Required selling price = Cost price + 60% of cost price

Use total SP = SP₁ (for 256 kg) + SP₂ (for 64 kg)

Calculation:

Total CP = 320 × 115 = ₹36,800

Required total SP = 36,800 + (60% of 36,800) = 36,800 + 22,080 = ₹58,880

SP for 256 kg = 256 × 160 = ₹40,960

SP needed from 64 kg = 58,880 - 40,960 = ₹17,920

Price per kg for remaining = 17,920 ÷ 64 = ₹280

∴ He should sell the remaining quantity at ₹280 per kg.

Given:

Cost of the first variety of pulses (C1) = ₹66 per kg

Cost of the second variety of pulses (C2) = ₹88 per kg

Cost of the mixture (Cm) = ₹76 per kg

Calculation:

The required ratio = 12: 10

= 6: 5

∴ The correct answer is option (1).

Given:

Cost price of sugar 1 = ₹78/kg

Cost price of sugar 2 = ₹36/kg

Selling price of mixture = ₹86.8/kg

Profit = 24%

Formula used:

CP of mixture = SP ÷ (1 + profit%)

Allegation rule: \(\frac{\text{Costlier}}{\text{Cheaper}} = \frac{\text{Mean CP} - \text{CP of cheaper}}{\text{CP of costlier} - \text{Mean CP}}\)

Calculation:

⇒ CP of mixture = 86.8 ÷ 1.24 = ₹70

Apply allegation:

⇒  (70 − 36) : (78 − 70) = 34 : 8

∴ Required ratio = 34 : 8

Given:

Cost of sugar A = ₹74/kg

Cost of sugar B = ₹41/kg

Selling price of mixture = ₹85.8/kg

Profit = 30%

Formula Used:

Cost Price of Mixture (C.P.) = Selling Price / (1 + Profit%)

Ratio = (C.P. of Costlier – C.P. of Mixture) : (C.P. of Mixture – C.P. of Cheaper)

Calculation:

C.P. of Mixture = ₹85.8 / (1 + 30/100)

⇒ C.P. of Mixture = ₹85.8 / 1.3

⇒ C.P. of Mixture = ₹66

Ratio = (C.P. of Mixture – C.P. of Cheaper) : (C.P. of Costlier – C.P. of Mixture)

⇒ Ratio = (66 – 41) : (74 – 66)

⇒ Ratio = 25 : 8

The required ratio is 25:8.

Given Profit = 10%, Selling Price = Rs. 35.2

Cost Price = Selling Price/(1 + Profit%) = 35.2/(1 + 10%) = 35.2/(1 + 0.1) = 35.2/1.1 = Rs. 32

Now find the ratio in which the two varieties of sugar need to be mixed to get a cost price of Rs. 32

Using the formula for Allegations,

Quantity of lesser price/Quantity of higher price = (Average - Price of lesser quantity)/(Price of higher quantity Average)

⇒ (32 – 30)/(38 – 32) = 2/6 = 1 : 3

GIVEN:

The amount of wheat is 5 kg and the price is Rs18/kg

The amount of wheat is 2kg

The amount of wheat is 7 kg and the price is Rs20/kg

FORMULA USED:

Quantity in kg × amount per kg = Price in Rs.

CALCULATION :

Let the price of 2 kg wheat be Rs. y/kg then,

5 × 18 + 2 × y  = 7 × 20 

⇒ 90 + 2y = 140 

⇒ 2y = 50 

⇒ y = 25

∴ The price of costlier wheat is Rs25. 

Given:

S.P. of 1 kg of mixture = Rs. 9.24,

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Formula Used: 

C.P = S.P x 100/(100 + P%)

Calculation: 

C.P = Rs 9.24 x 100/(100 + 10%)

C.P= Rs 924 x 100/(110%)

C.P = Rs 8.4

By Rule of Alligation 

Ratio of quantities of 1st and 2nd kind = 1.4 : 0.6 = 7 : 3.

Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.

Then, 7 : 3 = x : 27

∴ x = (27 × 7)/3 = 63 kg.

∴ The quantity of sugar that should be mixed is 63 Kg

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Given:

Rate of the first type of rice = Rs.45/kg

Rate of the mixture of rice = Rs.50/kg

Formula used:

Average rate of product = Total price of product/quantity of product

Calculation:

Let rice of first type of rice = 3x

Rice of second type of rice = 2x

Rate of second type of rice = Rs.A/kg

According to the question:

⇒ {(45 × 3x) + (A × 2x)}/5x = 50

⇒ 135x + 2Ax = 50 × 5x

⇒ 135 + 2A = 250

⇒ 2A = 250 - 135 = 115

⇒ A = 115/2 = Rs.57.5/kg

∴ The correct answer is Rs.57.5/kg

Shortcut TrickCalculation:

Now,

⇒ (X - 50)/(50 - 45) = 3/2

⇒ 2 × (X - 50) = 3 × 5

⇒ 2X - 100 = 15

⇒ 2X  = (15 + 100)

⇒ X = 115/2 = Rs.57.5/kg

∴ The correct answer is Rs.57.5/kg

Given

Quantity of first type of wheat = 40 kg, Rate = Rs. 12.50/kg

Quantity of second type of wheat = 30 kg, Rate = Rs. 14/kg

Gain = 5%

Concept:

Cost Price = Total cost of wheat.

Selling Price = Cost Price + Profit. We need to find the selling price per kg.

Calculation:

Total cost of wheat = (40 ×  12.50) + (30 ×  14) = Rs. 920

⇒ Cost price per kg = Rs. 920/(40 + 30) = Rs. 13.14

⇒ Selling price per kg = Cost price per kg + 5% of Cost price per kg

= Rs. 13.14 + (5/100) × 13.14 = Rs. 13.80

Therefore, the rate per kg to sell the mixture to gain 5% on the whole is Rs. 13.80.

Detailed solution:- 

Rini mixed 'C1' and 'C2' in the ratio 2:3. 

Let's assume that the cost per unit of 'C2' is Rs. ''. 

Cost of 2 units of 'C1' = 2 ×  Rs. 500 = Rs. 1000

Cost of 3 units of 'C2' = 3 × Rs. x = 3x

According to the question,

Rini is selling the mixture at the break-even price of Rs. 650 per unit. 

Total cost = Rs. 1000 + 3x ...... (1)

Total cost = (Selling price per unit ) × (Number of units sold Total cost)
 
⇒  Rs. 650 ×  5 ....(2)
(since the ratio is 2:3, so the total number of units is 2 + 3 = 5)

Now, we can set up the equation

⇒ 1000 + 3x =  650 ×  5 

⇒ 3x =  3250 - 1000

⇒ x =  2250 / 3 = Rs. 750

∴ The rate per unit of the second color, 'C2', is Rs. 750.

Shortcut Trick 

Given: 

CP of 90 kg sugar = Rs.14.50/kg 

CP of 110 kg sugar = Rs.18/kg 

Required Profit percent = 16%

Calculation: 

Cost price of the mixture = (90 kg × Rs.14.5 + 110 kg × Rs.18)/ (90 kg + 110 kg)

⇒ 3285/200

⇒ Rs.16.425/kg 

Selling price of the mixture = 116/100 × 16.425 

⇒ Rs.19.053/kg 

∴ The selling price of the mixture at 16% profit is Rs.19.05/kg

Given:

Ratio of the price of a mobile and a speaker is 5 : 2

Average price of two mobiles and a speaker is Rs. 20000

Formula Used:

Average = (sum of all the observations)/(total number of observations)

Calculation:

Let the price of a mobile and a speaker be Rs. 5M and Rs. 2M respectively.

According to the question,

Average price of two mobiles and a speaker is Rs. 20000

⇒ (2 × 5M + 2M)/3 = 20000

⇒ 10M + 2M = 60000

⇒ M = 5000

⇒ Price of a mobile = 5 × 5000 = Rs. 25000

⇒ Price of a speaker = 2 × 5000 = Rs.10000

∴ Required sum = 25000 + 10000 = Rs. 35000

Given:

A shopkeeper mixed low-quality vegetable oil costing Rs. 40 per litre with sunflower refined oil costing Rs. 80 per litre in the ratio of 2 ∶ 3 respectively

Calculation:

Let the total quantity of the mixture be 10 ltr.

10 litres of mixture contains,

⇒ (2/5) × 10 = 4 litres of low quality vegetable oil

⇒ (3/5) × 10 = 6 litres of sunflower refined oil

The cost price of 10 litres mixture = 4 × 40 + 6 × 80 = 160 + 480 = Rs. 640

The cost price of 1 litre mixture = 640/10 = Rs. 64

Profit earned = 100 – 64 = Rs. 36

Profit percentage = (36/64) × 100 = 56.25%

∴ the correct answer is 56.25%

Alternate Solution:

Let the cost price of the mixture be Rs. x per litre.

⇒ (80 - x) / (x - 40) = 2/3

⇒ 240 - 3x = 2x - 80

⇒ x = Rs. 64 per litre.

The selling price of the mixture = Rs. 100 per litre.

∴ Profit percentage = {(100 - 64) / 64} × 100 = 56.25%

Since, the shopkeeper mixed 200 ml water in 1 litre of milk, then he prepared (1000 + 200 = 1200 ml = 1.2 litre of milk-water mixture in Rs. 36

⇒ Cost price of 1 litre milk-water mixture = 36/1.2 = Rs. 30

Now, selling price of 1 litre milk-water mixture = Rs. 40

Profit earned per litre = 40 – 30 = Rs. 10