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A batswoman missed her century by four runs in an innings, in which the scoring shots in the form of sixes, fours, threes, twos and singles, were in the proportion 1 ∶ 3 ∶ 2 ∶ 7 ∶ 10. How many runs did she score in singles?

A batswoman missed her century by four runs in an innings, in which the scoring shots in the form of sixes, fours, threes, twos and singles, were in the proportion 1 ∶ 3 ∶ 2 ∶ 7 ∶ 10. How many runs did she score in singles? Correct Answer 20

Given:

A batswoman missed her century by four runs in an innings, in which the scoring shots in the form of sixes, fours, threes, twos, and singles, were in the proportion 1 ∶ 3 ∶ 2 ∶ 7 ∶ 10. 

Concept used:

Ratio Proportion

Century comprises 100 runs. 

Calculation:

Her score = 100 - 4 = 96 runs

Let the common ratio be Q.

Hence, the scoring shots in the form of sixes, fours, threes, twos, and singles were Q, 3Q,  2Q,  7Q, and 10Q.

According to the question,

Q × 6 + 3Q × 4 + 2Q × 3 + 7Q × 2 + 10Q = 96

⇒ 48Q = 96

⇒ Q = 2

⇒ 10Q = 20

∴ She scored in singles 20.

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