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Home » In an examination, the ratio of passes to failures was     . If     less had appeared and     less passed, the ratio of passes to failures would have been     . How many students appeared for the examination.
In an examination, the ratio of passes to failures was

    \[4:1\]

. If

    \[30\]

less had appeared and

    \[20\]

less passed, the ratio of passes to failures would have been

    \[5:1\]

. How many students appeared for the examination.
Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
In an examination, the ratio of passes to failures was

    \[4:1\]

. If

    \[30\]

less had appeared and

    \[20\]

less passed, the ratio of passes to failures would have been

    \[5:1\]

. How many students appeared for the examination.

Consider number of passes =

    \[4x\]

Number of failures = x

Total number of students appeared =

    \[4x\text{ }+\text{ }x\text{ }=\text{ }5x\]

In case

    \[2\]

Number of students appeared =

    \[5x\text{ }\text{ }30\]

Number of passes =

    \[4x\text{ }\text{ }20\]

So the number of failures =

    \[\left( 5x\text{ }\text{ }30 \right)\text{ }\text{ }\left( 4x\text{ }\text{ }20 \right)\]

By further calculation

    \[\begin{array}{*{35}{l}} =\text{ }5x\text{ }\text{ }30\text{ }\text{ }4x\text{ }+\text{ }20 \\ =\text{ }x\text{ }\text{ }10 \\ \end{array}\]

Based on the condition

    \[\left( 4x\text{ }\text{ }20 \right)/\text{ }\left( x\text{ }\text{ }10 \right)\text{ }=\text{ }5/1\]

By cross multiplication

    \[\begin{array}{*{35}{l}} 5x\text{ }\text{ }50\text{ }=\text{ }4x\text{ }\text{ }20 \\ 5x\text{ }\text{ }4x\text{ }=\text{ }\text{ }20\text{ }+\text{ }50 \\ x\text{ }=\text{ }30 \\ \end{array}\]

Number of students appeared =

    \[5x\text{ }=\text{ }5\text{ }\times \text{ }30\text{ }=\text{ }150\]

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