[100 points] In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many point

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Aptitude

TNPSC G4

10th CBSE Maths

In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?

120 points

90 points

80 points

100 points

Explanation:

Let x points make the game

A can give B 20 points, A can give C 32 points

=> When A scores x points, B scores $\left(x-20\right)$ points and C scores $\left(x-32\right)$ points
B can give C 15 points
=> When B scores x points, C scores $\left(x-15\right)$ points
$\text{=> When B scores 1 point, C scores }\dfrac{(x-15)}{x}\text{ points}$
$\text{=> When B scores $\left(x-20\right)$ point, C scores }\dfrac{(x-20)(x-15)}{x}\text{ points}$
$\text{i.e., } \left(x-32\right) = \dfrac{(x-20)(x-15)}{x}$
$\Rightarrow x(x-32) = (x-20)(x-15)$
$\Rightarrow x^2 - 32x = x^2 - 35x + 300$
$\Rightarrow - 32x = - 35x + 300$
$\Rightarrow 3x = 300$
$\Rightarrow x = 100$
i.e., 100 points make the game

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Important Links

In a game A can give B 20 points in 60 and C 18 points in 90. How many points can C give B in a game of 120?	Answer
In a km race A can beat B by 100 m and B can beat C by 60 m. In the same race A can beat C by	Answer
In a flat race, A beats B by 15 metres and C by 29 metres. When B and C run over the course together, B wins by 15 metres. Find the length of the course	Answer
A can run a kilometre in 4 min 54 sec and B in 5 min. How many metres start can A give B in a km race so that the race may end in a dead heat?	Answer
A runs 1 $\dfrac{3}{8}$ times As fast as B. If A gives B a start of 90 m and they reach the goal at the same time. The goal is at a distance of	Answer
In a 100 m race, A runs at 6 km/hr. A gives B a start of 4 m and still beats him by 4 sec. Find the speed of B.	Answer
Two boys A and B run at 4 1⁄5 and 8 km an hour respectively. A having 150 m start and the course being 1 km, B wins by a distance of	Answer
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In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?	Answer