In what ratio should two varieties of sugar at Rs.18 per kg and Rs.24 Kg be mixed together to get a mixture whose cost is Rs.20 per kg?

Correct Answer: 193 : 122

Explanation:

Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total content = 3,5,7

 

Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3 = 35 , 105/5 = 21 , 105/7 = 15

 

Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)

 i.e (35,70), (42,63), (45,60)

 

So overall mixture ratio of milk and water is

35+42+45 : 70+63+60

122:193

 

But in the question asked the ratio of water to milk = 193 : 122

Correct Answer: 27 %

Explanation:

Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135  
X = 27

So, required percentage of benzene = 27 %

Correct Answer: 3:2

Explanation:

Concentration of glucose are in the ratio = 1 2 : 3 5 : 4 5

Quantity of glucose taken from A = 1 liter out of 2

Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit

Quantity of glucose taken from C = 0.8 lit

So, total quantity of glucose taken from A,B and C = 3.6 lit

So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit

Ratio of glucose to alcohol = 3.6/2.4 = 3:2

Correct Answer: 7:3

Explanation:

Ratio of Milk and water in a vessel A is 4 : 1

 

Ratio of Milk and water in a vessel B is 3 : 2

 

Ratio of only milk in vessel A = 4 : 5

 

Ratio of only milk in vessel B = 3 : 5

 

Let 'x' be the quantity of milk in vessel C

 

Now as equal quantities are taken out from both vessels A & B

 

=> 4/5     :     3/5
               x 
  3/5-x          x - 4/5

 

=> 3 5 - x x - 4 5 = 1 1 (equal quantities)

 

=> x = 7/10

 

Therefore, quantity of milk in vessel C  = 7

 

=> Water quantity = 10 - 7 = 3

 

Hence the ratio of milk & water in vessel 3 is 7 : 3 

Correct Answer: 2 lit

Explanation:

Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres.

 

After adding water, juice would form 87.5% of the mixture.

 

Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72 

 

Hence 72 - 70 = 2 litres of water must be added.

Correct Answer: 7:5

Explanation:

Milk in 1-litre mixture of A = 4/7 litre. 

Milk in 1-litre mixture of B = 2/5 litre. 

Milk in 1-litre mixture of C = 1/2 litre.

 

By rule of alligation we have required ratio X:Y   

   X                  :                 Y  

  4/7                                2/5  

           \                      /

              (Mean ratio)
                   (1/2) 

           /                      \

 (1/2 ? 2/5)     :       (4/7 ? 1/2)  

    1/10                      1/1 4 

 

So Required ratio = X : Y = 1/10 : 1/14 = 7:5

Correct Answer: 50 gm

Explanation:

Initial quantity of copper = 80 100 x 50 = 40 g 

And that of Bronze = 50 - 40 = 10 g

Let 'p' gm of copper is added to the mixture

=> 50 + p x 90 100 = 40 + p

=> 45 + 0.9p = 40 + p

=> p = 50 g

Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.

Correct Answer: 25%

Explanation:

As water costs free, water sold at cost price of milk gives the profit.

Required profit % = 5/20 x 100 = 5 x 5 = 25%.

Correct Answer: 11:9

Explanation:

From the given data,

 

The part of honey in the first mixture = 1/4

 

The part of honey in the second mixture = 3/4

 

Let the part of honey in the third mixture = x

 

Then,

 

1/4             3/4

 

           x

 

(3/4)-x     x-(1/4) 

 

Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3

 

=>  3 4 - x x - 1 4 = 2 3

 

=> Solving we get the part of honey in the third mixture as 11/20

 

=> the remaining part of the mixture is water = 9/20

 

Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .

Correct Answer: 2:1

Explanation:

Given rate of wheat at cheap = Rs. 2.90/kg

Rate of wheat at cost = Rs. 3.20/kg

Mixture rate = Rs. 3/kg

Ratio of mixture = 

          2.90                              3.20

                              3

(3.20 - 3 = 0.20)            (3 - 2.90 = 0.10)

 

0.20 : 0.10 = 2:1

 

Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.