A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs 250 a quintal, the total monthly expenses of the family are Rs 1000 and when it is Rs 240 a quintal, the total monthly expenses are Rs 980. Find the total monthly expenses of the family when the cost of wheat is Rs 250 a quintal.
Answer: C Let constant expenses o the family = E, and they buy x amount of wheat Then, E + x*250 =1000 E + x*240 = 980 On solving we get, x=2 and E= 500 Total expenses = E + x* 350 = 500+ 2*350 = Rs 1200
Q. No. 14:
In three vessels, the ratio of water and milk is 6:7, 5:9 and 8:7 respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?
Answer: B Proportion of water = 6/13 + 5/14 + 8/15 = 3691/2730 Proportion of milk = 7/13 + 9/14 + 7/15 = 4499/2730 Required ratio = 3691:4499
Q. No. 15:
Railways fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8:6:3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12 respectively. If during a year, the ratio between passenger of 1st, 2nd and 3rd classes was 9:12:26 and total amount collected by the sale of tickets was Rs 1088, then find the collection from the passengers of 1st class.
Answer: D New ratio of fares (1st, 2nd and 3rd) => 8*1/5 : 6*11/12 : 3*1 => 40 : 33 :18 Ratio of passengers = 9 : 12 : 26 Ratio of amount collected = 40*9 : 12*33 : 26*18 => 90 : 99 : 117 Amount collected from 1st class fares = 90/306 * 1088 = Rs 320.
Q. No. 16:
In two alloys, the ratio of iron and copper is 4:3 and 6:1 respectively. If 14 kg of the first alloy and 42 kg of the second alloy is mixed together to form a new alloy, then what will be the ratio of copper to iron in the new alloy?
Answer: A In the new alloy total iron will be 44kg and copper will be 12 kg. Since iron = 8+36 =44 and copper = (44+12) - (8+36) = 12 Ratio of copper to iron = 12:44 => 3:11
Q. No. 17:
There are two identical vessels A and B. B is filled with water to brim and A is empty. There are two pails X and Y. Such that Y can hold half as much water as X. One operation is said to be executed when water is transferred from B to X using X once and water X is transferred to B from A using Y once. If a can hold 1/2 a litre of water and if takes 40 operations to equate the water level in A and B, what is the total volume of water in the system?
Answer: C 40*1/2 =20. As water in both are equal, there is 40L in the full system.
Q. No. 18:
Two vessels contains mixtures of milk and water in the ratio 8:1 and 1:5 respectively. The contents of both of these are mixed in a specific ration into a third vessel. How much mixture must be drawn from the second vessel to fill the third vessel(capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?
Answer: B Let us take 18 in each (LCM of 6 and 9) Then milk ratio in the two containers is 16:3. In the third vessel the ration is 9:9. So applying allegation, we get the ration 6:7 Required quantity = 7/13 * 26 = 14.