- Cost of fencing the circular field along its circumference at the rate of Rs.25 per meter is Rs.7200. A circular path of 2 meters width is contructed outside the circular field. Find the cost of paving the path at the rate of Rs.32 per square meter. Take pi = 3.
Circumference of the circular field = 7200/25
= 288 m
Radius of the circular field = 288/6 = 48 m
Area of the circular field = 3*48*48 = 6912 m^2
Areas of the circular field along with path = 3*(48+2)^2 = 7500 m^2
Areas of the path = 7500 – 6912 = 588 m^2
Cost of paving the path = 32*588 = Rs.18,816
- The total number of men, women and children working in a factory is 18. They earn Rs.4000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18:10:12 and if the wages of an individual man, woman and child is in the ratio 6:5:3. How much a women earn in a day.
Ratio of the number of men, women and children = 18/6:10/5:2/3
Now, (3x+2x+4x) = 18
=> x = 2
Share of all women = 10/40*4000 = Rs.1000
Share of each women = 1000/4 = Rs.250
- The ratio of present age of Sheeraj and Ram is 4:5 resp. while Sheeraj is 12 years older than Raj . If the ratio of present age of Raj to present age of Sheeraj is 1:2. What will be the age of Raj after 18 years?
48 years33 years42 years25 years30 yearsOption A
Let the present age of Sheeraj and Ram be 4x and 5x years.
Present age of Raj = 4x – 12 Now, 8x – 24 = 4x
=> x = 6
Age of Ram after 18 years = 5x+18 = 48 years
- Time taken by a boat to reach point B from point A is 4 hours while from point B to point A is 3.5 hours. If distance between point A and point B is 140 km, find the time taken by boat to travel 300 km in still water.
9 hours10 hours6 hours8 hours5 hoursOption D
Upstream speed of the boat = 140/4 = 35 km/hr.
Downstream speed of the boat = 140/3.5 = 40 km/hr.
Speed of boat in still water = (35+40)/2 = 37.5 km
Required time taken = 300/37.5 = 8 hours
- In an empty container, water and milk has been mixed in the ratio of x:18 resp. If 100 litres of mixture is replaced with 16 litres of water then the ratio of water to milk becomes 1:2 resp. Find the value of x, if the resultant amount of milk in the container is 144 litres.
Resultant amount of water = ½*144 = 72 litres
Now,x/18 = 56/144
=> x = 7
- A,B and C started a business with initial investments of Rs. 3000, Rs.3200 and Rs.3500 resp. After one year, A,B and C made additional investments of Rs.x+150 , Rs.x+300 and Rs.x+250 resp. Find the profit share of B out of the total profit of Rs. 4320 after two years.
Respective ratio of the profits of A,B and C
= 3000 + 3000+ x + 150 : 3200+3200+x+300 : 3500+3500+x+250
= 6150 + x: 6700+x : 7250+x
Profit share of B = (6700+x)/(20100+3x)*4320 = Rs.1440
- Rajan marked an article at 65% above the cost price and sold it after two consecutive discounts of ‘x%’ and 25%. In this transaction Rajan had a loss of 1%. Vishal marked the same article ‘x+10’% above the cost price and sold it after a discount of 10%. Find the profit percent earned by Vishal in this transaction.
Let CP be Rs.100.
SP of the article = 165*0.75*(100-x)/100 = 99
=> x = 20
MP of the article = 1.30*100 = Rs.130
SP = 130*0.90 = Rs.117
Profit% = (117-100)/100*100 = 17%
- A started from Ghaziabad to Gurgaon, and at the same time B started from Gurgaon to Ghaziabad. After reaching their respective destinations, they turned back to their starting places. If they met first time at a distance of 240 km from Ghaziabad and second time they met at Ghaziabad. Find the distance between Ghaziabad to Gurgaon.
Let the distance between these two places be x km.
Let the speed of A be p km/hr. and B be q km/hr.
240/p = (x-240)/q
=> q/p = 1/2
Now, (x-240)/240 = ½
=> x = 360
- A national team of 6 players is to be selected from a group of 5,4,6 and 5 players from east , west , north and south zones resp. In how many ways a team having exactly 2 players from east zone and at least one player from each zone can be selected?
Number of ways
= 5C2*4C2*6C1*5C1 + 5C2*4C2*6C2*5C1 + 5C2*4C1*6C1*5C2
= 1800 + 3000 + 2400 = 7200
- Two cards are randomly drawn from well-shuffled deck of 52 cards. What is the probability that both the cards drawn are either face cards or red in colour?
Required Probability = 26C2/52C2 + 12C2/52C2 – 6C2/52C2
= 25/102 + 11/221 – 5/442 = 188/663