Question 1

Tea worth of Rs. 135/kg and Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?

Accepted Answer

To solve the problem, let's define the prices and quantities of the different varieties of tea being mixed. Given: Price of the first variety of tea = Rs. 135/kg Price of the second variety of tea = Rs. 126/kg Ratio of the first, second, and third varieties = 1 : 1 : 2 Let the price of the third variety of tea be x x x Rs./kg. The total mixture is worth Rs. 153/kg. Since the ratio of the tea varieties is 1:1:2, we can assume the quantities of each type of tea in the mixture to be: Quantity of the first variety = 1 unit Quantity of the second variety = 1 unit Quantity of the third variety = 2 units The total cost of the mixture can be expressed as the weighted average cost of the individual varieties based on their respective quantities. Let's compute the cost per unit for the mixture: Total cost = ( 1 unit × 135 Rs./kg ) + ( 1 unit × 126 Rs./kg ) + ( 2 units × x Rs./kg ) 	ext{Total cost} = (1 	ext{ unit} 	imes 135 	ext{ Rs./kg}) + (1 	ext{ unit} 	imes 126 	ext{ Rs./kg}) + (2 	ext{ units} 	imes x 	ext{ Rs./kg}) Total cost=(1 unit×135 Rs./kg)+(1 unit×126 Rs./kg)+(2 units×x Rs./kg) The total quantity of the mixture is: 1 unit + 1 unit + 2 units = 4 units 1 	ext{ unit} + 1 	ext{ unit} + 2 	ext{ units} = 4 	ext{ units} 1 unit+1 unit+2 units=4 units The average price per kg of the mixture is given as Rs. 153. Therefore, we set up the equation: 135 + 126 + 2 x 4 = 153 \frac{135 + 126 + 2x}{4} = 153 4135+126+2x=153 First, simplify the numerator: 135 + 126 + 2 x = 261 + 2 x 135 + 126 + 2x = 261 + 2x 135+126+2x=261+2x Next, substitute this back into the equation and solve for x x x: 261 + 2 x 4 = 153 \frac{261 + 2x}{4} = 153 4261+2x=153 Multiply both sides by 4 to clear the denominator: 261 + 2 x = 612 261 + 2x = 612 261+2x=612 Now, isolate x x x: 2 x = 612 − 261 2x = 612 - 261 2x=612−261 2 x = 351 2x = 351 2x=351 x = 351 2 x = \frac{351}{2} x=2351 x = 175.5 x = 175.5 x=175.5 Thus, the price of the third variety of tea is Rs. 175.50 per kg.

Question 2

A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Accepted Answer

Suppose the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water. Quantity of water in new mixture = 3 - 3 x 8 + x litres. Quantity of syrup in new mixture = 5 - 5 x 8 litres. 3 - 3 x 8 + x = 5 - 5 x 8 => 5x + 24 = 40 - 5x => 10x = 16 => x = 8/5 So, part of the mixture replaced = 8 5 × 1 8 = 1/5.

Question 3

The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?

Accepted Answer

Therefore x = 21%

Question 4

A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

Accepted Answer

Number of liters of water in 125 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters Let us Assume that another 'P' liters of water are added to the mixture to make water 25% of the new mixture. So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P) Thus, (30 + P) = 25% of (150 + P) Solving, we get P = 10 liters

Question 5

How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg?

Accepted Answer

By the rule of alligation: C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.

Question 6

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

Accepted Answer

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 ∴ (20-x)/(x-15) = 2/3 ⇒ 60 - 3x = 2x - 30 ⇒ x = 18.

Question 7

The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water…

Accepted Answer

Wine Water 8L 32L 1 : 4 20 % 80% (original ratio) 30 % 70% (required ratio) In ths case, the percentage of water being reduced when the mixture is being replaced with wine. so the ratio of left quantity to the initial quantity is 7:8 Therefore , 7 8 = 1 - K 40 => K = 5 Lit

Question 8

The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:

Accepted Answer

pool : kerosene 3 : 2(initially) 2 : 3(after replacement) R e m a i n i n g Q u a n t i t y I n i t i a l Q u a n t i t y = 1 - R e p l a c e d Q u a n t i t y T o t a l Q u a n t i t y (for petrol) 2 3 = 1 - 10 k => K = 30 Therefore the total quantity of the mixture in the container is 30 liters.

Question 9

A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :

Accepted Answer

Profit (%) = 9.09 % = 1/11 Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

Question 10

The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

Accepted Answer

Total no.of boys : no. of girls = 13:27 27 : 13

Question 11

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

Accepted Answer

By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3

Question 12

The ratio of water and alcohol in two different containers is 2:3 and 4:5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7:5?

Accepted Answer

W 1 : A 1 W 2 : A 2 . . . . . W N : A N 2 : 3 4 : 5 5 : 7 W 1 W 1 + A 1 = 2 5 W 2 W 2 + A 2 = 4 9 W N W N + A N = 5 12 = 72/180 = 80/180 = 75/180 => 5 : 3 Therefore, the ratio is 5: 3

Question 13

In the 75 litres of mixture of milk and water, the ratio of milk and water is 4:1. The quantity of water required to make the ratio of milk and water 3:1 is

Accepted Answer

Total quantity of mixture = 75 litre Milk : Water = 4 : 1 3 : 1

Question 14

From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of …

Accepted Answer

Let quantity of mixture be x liters. Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid = x 1 - y x n units, Where n = no of operations . So, Quantity of Milk = x 1 - 6 x 2 Given that, Milk : Water = 9 : 16 => Milk : (Milk + Water) = 9 : (9+16) => Milk : Mixture = 9 : 25 Therefore, x 1 - 6 x 2 x = 9 25 => x = 15 liters

Question 15

In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot?

Accepted Answer

Let the capacity of the pot be 'P' litres. Quantity of milk in the mixture before adding milk = 4/9 (P - 8) After adding milk, quantity of milk in the mixture = 6/11 P. 6P/11 - 8 = 4/9(P - 8) 10P = 792 - 352 => P = 44. The capacity of the pot is 44 liters.

Question 16

A sum of Rs.118 was divided among 50 boys and girls such that each boy received Rs.2.60 and each girl Rs.1.80. Find the number of boys and girls?

Accepted Answer

Average money received by each = 118/50 = Rs. 2.36 Therefore, Ratio of No.of boys and girls = 56 : 24 = 7 : 3 Therefore, Number of boys = 50 x (7/10) = 35 Number of girls = 50 - 35 = 15

Question 17

In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 liters of pure milk , the percentage of milk in the mixture become 76%. The quantity of mixture is:

Accepted Answer

Milk Water 74% 26% (initially) 76% 24% ( after replacement) Left amount = Initial amount 1 - r e p l a c e d a m o u n t t o t a l a m o u n t 24 = 26 1 - 7 k => k = 91

Question 18

Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture?

Accepted Answer

From the given data, let the initial quantity of the mixture = 5x Then, 2 x - 16 3 x - 24 + 40 = 1 4 8 x - 64 = 3 x + 16 5 x = 80 x = 16 lit Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.

Question 19

From a container of wine, a thief has stolen 15 liters of wine and replaced it with same quantity of water.He again repeated the same process. Thus in three attempts the ratio of wine and water became 343:169. The initial amount of wine in the conta…

Accepted Answer

W i n e ( l e f t ) W a t e r ( a d d e d ) = 343 169 It means W i n e ( l e f t ) W i n e ( i n i t i a l a m o u n t ) = 343 512 ∵ 343 + 169 = 512 Thus , 343 x = 512 x 1 - 15 K 3 ⇒ 343 512 = 7 8 3 = 1 - 15 k 3 => K = 120 Thus the initial amount of wine was 120 liters.

Alligation or Mixture Questions