Directions: Refer the following data to answer the questions given below.
Solution:
Le the c.p of milk be Re.1 per litre. ...(A)
Now, milk in 1 litre mixture of X = 11/15 ...(1)
Then c.p of 1 litre mixture of X = (11/15) x 1 = Re.11/15 (Based on value in previous equation and our assumption A)
Milk in 1 litre mixture of Y = 3/5 ...(2)
Then c.p of 1 litre mixture of Y = (3/5) x 1 = Re.3/5 (Based on value in previous equation and our assumption A)
As given in question, milk and water in final mixture are in the ration 2:1. Therefore, Milk in 1 litre mixture of Z = 2/(1 + 2) x 1 = 2/3. ...(3)
Then the c.p of 1 litre mixture of Z = Re.2/3 (Based on value in previous equation and our assumption A)
Here, d = 11/15, c = 3/5 and m = 2/3
Then d - m = 11/15 - 2/3 = (11-10)/15 = 1/15
and m - c = 2/3 - 3/5 = (10-9)/15 = 1/15
Required ratio (as per our formula) = d-m : m-c = 1/15 : 1/15 = 1:1
Hence 1:1 is the required ratio.
Directions: Refer the following data to answer the questions given below.
Solution: The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk. Let W_o be the amount of water in the mixture originally = 8 litres. Let W_r be the amount of water in the mixture after the replacements have taken place. Then, Wr/Wo=(1−{R/M})n, where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, Wr/Wo=(1/2)2=1/4 Therefore, Wr=Wo/4=8/4=2litres Hence the mixture will have 18 litres of milk and 2 litres of water.
Directions: Refer the following data to answer the questions given below.
Step 1: As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.
Step 2: C.P of 1 kg of rice of 1st kind = Rs. 42
C.P of 1 kg of rice of 2nd kind = Rs. 24
Mean price = Rs. 40
Directions: Refer the following data to answer the questions given below.
By alligation rule:
Quantityof1stkindofwheat/Quantityof2ndkindofwheat=3/21=1/7
So they must be mixed in the ratio 1 : 7
Thus,
Quantityof2ndkindofwheat/Quantityof3rdkindofwheat=(
Quantityof1stkindofwheat/Quantityof3rdkindofwheat)×(Quantityof2ndkindofwheat/Quantityof1stkindofwheat)
⇒ Quantityof2ndkindofwheat/Quantityof3rdkindofwheat=(11/7x7/1)=(11/1)
Thus, Quantities of wheat of 1st : 2nd : 3rd = 11 : 77 : 7
Directions: Refer the following data to answer the questions given below.
Solution:
30 litres of the mixture has milk and water in the ratio 7 : 3. i.e. the solution has 21 litres of milk and 9 litres of water.
When you add more water, the amount of milk in the mixture remains constant at 21 litres. In the first case, before addition of further water, 21 litres of milk accounts for 70% by volume. After water is added, the new mixture contains 60% milk and 40% water.
Therefore, the 21 litres of milk accounts for 60% by volume.
Hence, 100% volume = 21/0.6=35litres.
We started with 30 litres and ended up with 35 litres. Therefore, 5 litres of water was added.