Correct Answer: 6 ml

Explanation:

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7
Let x ml of water be added
We get,
4 . 5 4 . 5 + x = 3 7
=> x=6
Hence 6ml of water is added.

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: 7:3

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: 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: 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: 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: 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.

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: 3:2

Explanation:

Let he mixes the oils in the ratio = x : y

Then, the cost price of the oils = 60x + 65y

Given selling price = Rs. 68.20

=> Selling price = 68.20(x+y)

Given profit = 10% = SP - CP

=> 10/100 (60x + 65y) = 68.20(x+y)-(60x + 65y)

=> 6x + 6.5y = 8.20x + 3.20y

=>2.2x = 3.3y

=> x : y = 3 : 2

Correct Answer: 60 lit