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The runs scored by four cricketers A, B, C and D for West Indies in an innings were in the ratio 5 : 2 : 4 : 3. The remaining players scored half the total of these four players. If D had scored 23 runs more than B, what was the total score of Sri Lanka which scored 2/3 that of West Indies?

The runs scored by four cricketers A, B, C and D for West Indies in an innings were in the ratio 5 : 2 : 4 : 3. The remaining players scored half the total of these four players. If D had scored 23 runs more than B, what was the total score of Sri Lanka which scored 2/3 that of West Indies? Correct Answer 322

Given :

The ratio of run scored by four players is 5 : 2 : 4 : 3

D scored 23 runs more than B

The remaining player scored half of the total runs scored by these 4 players.

Solution :

Let run scored by A be 5x

Let run scored by B be 2x

Let run scored by C be 4x

Let run scored by D be 3x

A.T.Q.,

D scored 23 runs more than B

⇒ 3x - 2x = 23

⇒ x = 23     ----(1)

Run scored by these four players = 5x + 2x + 4x + 3x

⇒ Run scored by these four players = 14x

⇒ Run scored by these four players = 14 × 23     (from 1)

⇒ Run scored by these four players = 322     ----(2)

The remaining player scored half of the run scored by these four players

⇒ Run scored by remaining players = 322/2

⇒ Run scored by remaining players = 161     ----(3)

⇒ The total run scored by the team West Indies = 322 + 161

⇒ Total runs scored by the team West Indies = 483

⇒ Total runs scored by the team Sri Lanka = (2/3) × 483

∴ The total runs scored by the team Sri Lanka is 322.

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