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In a race where 12 cars are running, the chance that car X will win is $$\frac{1}{6},$$ that Y will win is $$\frac{{1}}{{10}}$$ and that Z will win is $$\frac{{1}}{{8}}$$. Assuming that a dead heat is impossible. Find the chance that one of them will win.

Correct Answer: $$\frac{{47}}{{120}}$$
Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive)
$$\eqalign{ & = \frac{1}{6} + \frac{1}{{10}} + \frac{1}{8} \cr & = \frac{{47}}{{120}} \cr} $$

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?

John, Jack, Joseph and Jordan participated in a running race. Only the winner finished the race in 10 minutes. Which two pieces of information can tell you who the winner was? (i) John finished the race in 16 minutes . (ii) Joseph finished the race earlier than Jack by 2 minutes. (iii) Jack finished the race later than Jordan by 4 minutes. (iv) Jordan finished the race earlier than John by 6 minutes. (v) John finished the race later than Joseph by minutes.

Two cars start simultaneously from cities A and B, towards B and A respectively, on the same route. Once the two cars reach their destinations they turned around and move towards the other city without any loss of time. The two cars continue shuttling in this manner for exactly 20 hours. If the speed of the car starting from A is 60km/hr and the speed of the car starting from B is 40km/hr and the distance between the two cities is 120 km, find the number of times the two cars cross each other?

A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 50% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?

There are 1250 cars in a factory. The factory produces 5 cars hourly. If the sales of the factory are 50 cars per day, what will be the sale percentage to the total cars held by the factory after 5 days. It is known that the factory runs 8 hours daily.

All dolls are windows.All bottles are windows.All cars are bottles. 1. All cars are windows 2. some cars are dolls 3. some windows are cars Which among the above listed are true

Statements : All dolls are windows. All bottles are windows. All cars are bottles.

Conclusions :
I. All cars are windows.
II. Some cars are dolls.
III. Some windows are cars.

Statements : No mat is fan. Some fans are cars. All cars are shirts.

Conclusions :
I. All mats are cars.
II. All shirts are cars.
III. Some shirts are fans.
IV. No shirt is a mat.

Statements : Some cars are jeeps. All the boxes are jeeps. All the pens are cars.

Conclusions :
I. Some cars are boxes.
II. No pen is jeep.
III. Some boxes are cars.

In a race, the odd favour of cars P,Q,R,S are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of them wins the race.