Test Index

Ratio and Proportion

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Question : 61 of 112

Marks: +1, -0

The highest score in an innings was

\;\frac{2}{9}

of the total score and the next highest was

\;\frac{2}{9}

of the remainder. These score differed by 8 runs. What was the total score in the innings?

162
152
142
1132

Solution:

Concept:

Find total score using given fractional differences.

Explanation:

Let total score be

T

.

Highest score is

\frac{2}{9}T

.

Remainder after highest:

T - \frac{2}{9}T = \frac{7}{9}T

.

Next highest is

\frac{2}{9}

of remainder:

\frac{2}{9} \times \frac{7}{9}T = \frac{14}{81}T

.

Difference between scores:

\frac{2}{9}T - \frac{14}{81}T = \frac{18}{81}T - \frac{14}{81}T = \frac{4}{81}T

.

This equals 8 runs:

\frac{4}{81}T = 8

.

Solve:

T = 8 \times \frac{81}{4} = 2 \times 81 = 162

.

Answer:

162

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