Bright Zoom Maths

Aptitude Solved Problems 1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Answer: 25200 Explanation: Number of ways of selecting 3 consonants from 7 = 7C3 Number of ways of selecting 2 vowels from 4 = 4C2 Number of ways of selecting 3 consonants from 7 and 2 vowels from 4 = 7C3 * 4C2 = ( 7 * 6 * 5 ) / ( 3 * 2 * 1 ) * ( 4 * 3) / ( 2 * 1 ) = 210 It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels). Number of ways of arranging 5 letters among themselves = 5! = ( 5 * 4 * 3 * 2 * 1 ) = 120 Hence, required number of ways = ( 210 * 120 ) = 25200 ∴ Required number of ways are 25200 2. A man can row 6 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. Find the distance of the place? Answer: 5.33 km Explanation: Speed downstream = ( 6 + 2 ) km / hr = 8 km / hr Speed upstream = ( 6 - 2 ) km / hr = 4 km / ...

Aptitude Solved Problems challenge your brain in aptitude!! 1. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs 4000, the new ratio becomes 40 : 57. What is Sumit present salary. Answer: Rs. 38000 Explanation: Let the original Salaries of Ravi and Sumit is 2x and 3x. ( 2 x + 4000 ) / ( 3 x + 4000 ) = ( 40 / 57 ) 57 ( 2x + 4000 ) = 40 ( 3x + 4000) ( 114 x + 228000 ) = ( 120 x + 160000 ) ( 228000 - 160000 ) = ( 120 x - 114 x ) 6 x = 68000 3 x = 34000 Sumit Salary = ( 3x + 4000 ) = ( 34000 + 4000 ) = 38000 ∴ Sumit present salary is Rs. 38000 2. The telephone bill of a certain establishment is party fixed and partly varies as the number of calls consumed. In a certain month 540 units are consumed and the bill is Rs.1800. In another month 620 units are consumed then the bill becomes Rs.2040. In another month 500 units are consumed due to more holidays. The bill for that month would be? Answer: Rs. 1680 Explanation: Let...

Brain Teaser !! How many birds are left on the branch? 1. There are nine children in the house, and only them in the house so A is ironing B is watching tv C is cooking D is playing chess E is bathing F is listening radio G is sleeping I is dressing What H is doing ? Answer: H is playing chess with D. 2. There are ten birds on a branch. and you shot one bird. how many birds are left on the branch? Answer: Because of the sound of the gun shot all other birds will also fly. 3. A man walks into his bathroom and shoots himself right between the eyes using the real gun with real bullets. He walks out alive, with no blood anywhere. And no, he didn′t miss and he was not superman, or any other caped crusader. How did he do this? Answer: He shot his image that he saw in the bathroom mirror! 4. A man is found hanging in a room 3 feet off the ground. There is nothing else in the room except for a large puddle of water on the ground. The police can′t see ...

Aptitude Solved Problems Find the rate of the stream? 1. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going? Answer: 9 seconds. Explanation: Speed of the train relative to man = ( 68 - 8 ) km/hr = 60 km/hr To convert km/hr to m/sec = ( 60 * ( 5 / 18 ) ) m/sec = ( 50 / 3 ) m/sec Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50 / 3 ) m/sec = ( 150 * ( 3 / 50 ) ) sec = 3 * 3 = 9 sec ∴ In 9 sec it will pass the man. 2. The average of a non - zero number & its square is 7 times the number . Then find the number? Answer: 13. Explanation: Let the number be x. ( x + x2 ) / 2 = 7x x + x2 = 7x * 2 x + x2 = 14x x + x2 - 14x = 0 x2 + x - 14x = 0 x2 - 13x = 0 x * ( x - 13 ) = 0 x = 0 ( or ) x - 13 = 0 Given that the number is non zero so x = 13 ∴ The number is 13. 3. Three partners P, Q and R invest a tota...

Aptitude Solved Problems 1. The ratio between the present ages of Arun and Aravind is 6 : 7. If Aravind is 4 years old than Arun, what will be the ratio of the ages of Arun and Aravind after 4 years? Answer: 7 : 8. Explanation: Let Arun age and Aravind age is 6x years and 7x years. 7x - 6x = 4 x = 4 Required ratio = ( 6x + 4 ) : ( 7x + 4 ) = [ ( 6 * 4 ) + 4 ] : [ ( 7 * 4 ) + 4 ] = ( 24 + 4 ) : ( 28 + 4 ) = 28 : 32 = 7 : 8 ∴ The ratio of the ages will be 7 : 8. 2. The volume of a cube is 729 cm3 . Find the surface area of a cube? Answer: 486 cm2. Explanation: Volume of a cube = a 3 cm3 729 cm3 = a3 cm3 a3 cm3 = 93 cm3 Taking cube root on both sides a = 9 cm The surface area of a cube = 6 a2 cm2 = 6 * ( 92) cm2 = ( 6 * 81 ) cm2 = 486 cm2 ∴ The surface area of a cube is 486 cm2. 3. The sum of three numbers is 123. If the ratio between first and second numbers is 2:5 and that of between second and third is 3:4, then find the difference between seco...

Solved Problems - Pipes And Cisterns 1. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty the full cistern? Answer: 10 minutes Explanation: Work done by a waste pipe in 1 minute = 1 / 20 - ( 1 / 12 + 1 / 15 ) = ( 3 - 5 - 4 ) / 60 = ( -6 / 60 ) = -1 / 10 ∴ Waste pipe will empty the full cistern = 10 minutes 2. Two pipes X and Y can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Answer: 18 hours Explanation: Part filled by X in 1 hour = 1 / 30 Part filled by Y in 1 hour = 1 / 45 Part filled by (X+Y) in 1 hour = 1 / 30 + 1 / 45 = ( 3 + 2 ) / 90 = 5 / 90 = 1 / 18 ∴ Both the pipes together will fill the tank = 18 hours 3. An electric pump can fill a tank in 2 hours. Because of a leak in the ...