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**Shortcut Tricks To Solve Race and Game**

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**Effective for all Banking Exam**

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**Trick – 1**

**In a game of billiards, A can give B ${{x}_{1}}$, points in x and A can give C ${{y}_{1}}$ in y. In a game of z, C can give B**

**Trick – 2**

**In a game of ’x’ points, A can give B ${{x}_{1}}$ points and C ${{x}_{2}}$ points (${{x}_{2}}$>${{x}_{1}}$), then B can give C**

**C $\left[ x\left( \frac{{{x}_{2}}-{{x}_{1}}}{x-{{x}_{1}}} \right) \right]po\operatorname{int}s$**

**Trick – 3**

**A beats B by ${{y}_{1}}$ metres and C by ${{y}_{2}}$ metres in a race of ${{x}_{1}}$ metres. In a race of ${{x}_{2}}$ metres C beats B by**

**$\left( \frac{{{y}_{1}}-{{y}_{2}}}{{{x}_{1}}-{{y}_{2}}} \right)\times {{x}_{2}}$ metres**

**Trick – 4**

**In a km race A beats B by X metres or t seconds. Then the time taken by A to complete the race is given by**

**$\frac{t}{x}(1000-x)seconds$**

**Trick – 5**

**A can run a km rate in x min and B in y min(y>x). The distance by which A can beat B is given by**

**$\left[ 1000\left( 1-\frac{x}{y} \right) \right]metres$**

**Trick – 6**

**In a 100 m race A runs at ‘x’ km/hr. A gives b a start of y metres and still beats him by ‘t’ seconds, then the speed of B is given by**

**$\frac{18}{5}\left[ \frac{(100-y)x}{360+xt} \right]km/hr.$**

**Questions for Practice**

**Q1. In a game of billiards, A can give B 12 points in 60 and A can give C 10 in 90. How many points C can give B in a game of 70 ?**

**Q2. In a game of 100 points, A can give B 25 points and C 31 points, then how many points can B give C ?**

**Q3. A beats B by 31 metres and C by 18 metres in a race of 200 metres. By how many metres will c beat B in a race of 350 metres ?**

**Q4. In a km race A beats B by 25 metres or 5 seconds. Find the time taken by A to complete the race**

**Q5. A can run a km rate in 3 min and B in 3 min 20 sec. By what distance can A beat B ?**

**Q6. In a 100m race A runs at 5 km/hr. A gives B a start of 8 metres and still beats him by 8 seconds. Find the speed of B.**

__Answers__**Answer 1. 7 points**

**Answer 2. 8 points**

**Answer 3. 25 m**

**Answer 4. 3 min 15 seconds**

**Answer 5. ( 3 min = 180 sec and 3 mi 20 sec = 200 seconds.)**

**Answer 6. 4.14 km/hr**

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