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# 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

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It is a question from ML aggarwal, class 10th, chapter 7, ratio and proportion, Avichal publication

In this ques we have been given the ratio of the passes to failures is given and their ratio gets changed if their number gets changes according to the question. We have to find the students appeared in the exam

Question 21

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1. Solution:

Consider number of passes = 4x

Number of failures = x

Total number of students appeared = 4x + x = 5x

In case 2

Number of students appeared = 5x – 30

Number of passes = 4x – 20

So the number of failures = (5x – 30) – (4x – 20)

By further calculation

= 5x – 30 – 4x + 20

= x – 10

Based on the condition

(4x – 20)/ (x – 10) = 5/1

By cross multiplication

5x – 50 = 4x – 20

5x – 4x = – 20 + 50

x = 30

Number of students appeared = 5x = 5 × 30 = 150

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