Test: Alligation & Mixture- 3 - CAT MCQ

Mixing Rs. 4/kg and Rs. 5/kg to get Rs. 4.6 per kg we get that the ratio of mixing is 2:3. If the first oil is 40 kg, the second would be 60 kg

Hence, by the rule of allegation they must be mixed in the ratio 40:60
if quantity of first type is 40kg , the quantity of second type will be 60 kg

In 125 gallons we have 25 gallons water and 100 gallons wine. To increase the percentage of water to 25%, we need to reduce the percentage of wine to 75%. This means that 100 gallons of wine = 75% of the new mixture. Thus the total mixture = 133.33 gallons. Thus, we need to mx 133.33 - 125 = 8.33 gallons of water in order to make the water equivalent to 25% of the mixture.

The ratio of boys and girls appearing for the exam can be seen to be 3:1 using the following alligation figure.

This means that out of 400 students, there must have been 100 girls who appeared in the exam.

From the figure it is clear that the ratio of the number of officers to the number of other employees would be 40:3400. Since there are 120 officers, there would be 3400 x 3 = 10200 workers in the company. Thus the total number of employees would be 10200 + 120 = 10320.

Amount of water left = 50 x 9/10 x 9/10 = 40.5 liters. Hence, wine = 9.5 liters. Ratio of wine and water = 19:81. Option (c) is correct.

It can be seen from the ratio 36:13 that the proportion of liquid soap to water is 36/49 after two mixings. This means that 6/7th of the liquid soap must have been allowed to remain in the container and hence l/7th of the conatiner’s original liquid soap would have been drawn out by the thief. Since he takes out 4 gallons every time, there must have been 28 gallons in the container. ( as 4 should be l/7th of 28)

The average value of a coin is 41 paise and there are only 20 paise and 50 paise coins in the sum. Hence, the ratio of the number of 20 paise coins to 50 paise coins would be 9:21 = 3:7. Since there are a total of 90 coins, the number of 20 paise coins would be 3 x 90/10 = 27 coins.

Solve using options. Initially there are 7 liters of water in 70 liters of the mixture. By mixing 2 liters of water we will have 9 liters of water in 72 liters of the mixture - which is exactly 12.5%.

By selling at 300 if we need to get a profit of 25% it means that the cost price would be 300/1.25 = 240.

Thus, in 52 quintals of the second we need to mix 26 quintals of the first.

The percentage of honey in the new mixture would be: (2 x 25 + 3 x 15)15 = 275/5 =55%. The ratio of honey to water in the new mixture would be 55:45 = 11:9.

Assume the capacity of the two containers is 198 liters each. When we mix 198 liters of the first and 198 liters of the second the amount of oil would be: 198 x 4/11 + 198 x 7/18 = 72 + 77 = 149 liters. Consequently the amount of water would be 396 - 149 = 247 liters. Option (a) is correct.

Solve using options as that would be the best way to tackle this question. Option (b) fits the situation perfectly as if we take the price of the pen as Rs. 25, the cost of the pencil would be Rs. 10. The profit in selling the pen would be Rs.5 while the loss in selling the pencil would be Rs. 1. The total profit would be Rs. 4 as stipulated by the problem.

The following visualization would help:

From the figure we can see that the original mixture would be 40 liters and the petrol being mixed is 8 liters. Thus, the vessel capacity is 48 liters.

If all the animals were ducks we would have 180 heads and 360 legs. If we reduce the number of ducks by 1 to 179 and increase the number of deers by 1 to 1, we would get an incremental 2 legs.
Since, the number of legs we need to increment is 88 (448 - 360 = 88), we need to have 44 deers and 136 ducks.