Q1. A bag contains three black and four red balls. Three balls are chosen randomly. Find the probability that at least one ball is black.
Q2. In how many different ways the letters of the word ‘SHELTER’ can be arranged such that S and R always come at end places?
Q3. Three men A, B and C working together 8 hours per day can print 900 pages in 20 days. In a day B prints as many pages more than A as C prints as many pages more than B. The number of pages printed by A in 4 hours equal to the number of pages printed by C in 1 hours. How many pages C prints in an hour?
Note : working hours for all men is 8 hours only.
Q4. The sum of digits of a two digit number is 1/5 of the difference between the number and the number obtained by interchanging the digits. What definitely is the difference b/w the digits of that number?
(d) Can’t be determined
Q5. The incomes of A, B and C are in the ratio of 7 : 9 : 12 and their expenses are in the ratio of 8 : 9 : 15. If A saves 1/4 of his income, then what is the ratio of their savings respectively?
(a) 59 : 99 : 69
(b) 56 : 99 : 69
(c) 56 : 99 : 96
(d) 65 : 99 : 69
Q6.In 6 litre mixture of spirit and water there is 15% water. In this mixture 4 litre of another mixture containing 10% water is mixed. After this 1.5 litre of spirit and 0.5 litre of water is mixed in this mixture. Find the percentage of water in the final mixture.
Q7.A milkman sells the milk at cost price but mixes water in the milk. In this way he earns 50/3% profit. In what ratio does he mix milk and water?
(a) 5 : 1
(b) 7 : 1
(c) 6 : 1
(d) 3 : 10
Q8.A can do 50% more work than B can do in the same time. B alone can do a piece of work in 20 hr. A, with the help of B, can finish the same work in how many hours?
Q9.A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5 galloons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will it take to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter).
(a) 7.14 min
(b) 10.0 min
(c) 10.7 min
(d) 5.0 min
Q10.A and B started a business in partnership by investing Rs 10,000 and Rs 4000 respectively. Condition of partnership is that B got Rs 100 per month for management of the business. Remaining profit has to be distributed in the ratio of their investments. Find the share of their profit, if the annual profit is Rs 4000.
(a) Rs 3000 each
(b) Rs 2500 each
(c) Rs 1500 each
(d) Rs 2000 each
Required no. of ways =5!/2!×2!
Final quantity of water in mixture
= 1.8 litre
∴ Required percentage =1.8/12×100
Ratio of efficiencies of A and B = 3 : 2
∴ One hour work of both A and B =1/20+3/(2×20)
i.e. A and B together will finish the work in 8 hrs.
Since rate of flow is proportional to Diameter
∴ Outlet rate of flow = 2 × 5
= 10 gallons/min
Time taken by outlet Pipe to empty the tank
Ratio of investments of A and B = 10,000 : 4000
= 5 : 2
Profit of A = 5x
Profit of B = 2x + 12 × 100
= 2x + 1200
∴ 5x + 2x + 1200 = 4000
⇒ x = 400
∴ Profit of A = 2000
Profit of B = 2000