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In an examination 52% of the candidates ...

In an examination 52% of the candidates failed in Science 42% in Mathematics and 17% in both. The no. of those who passed in both the subjects, is :

A

0.83

B

0.64

C

0.23

D

0.5555

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these calculations: ### Step 1: Understand the given percentages We know: - 52% of candidates failed in Science. - 42% of candidates failed in Mathematics. - 17% of candidates failed in both subjects. ### Step 2: Calculate the percentage of candidates who failed only in Science To find the percentage of candidates who failed only in Science, we subtract the percentage of candidates who failed in both subjects from the percentage who failed in Science: \[ \text{Failed only in Science} = \text{Failed in Science} - \text{Failed in both} \] \[ = 52\% - 17\% = 35\% \] ### Step 3: Calculate the percentage of candidates who failed only in Mathematics Similarly, to find the percentage of candidates who failed only in Mathematics, we subtract the percentage of candidates who failed in both subjects from the percentage who failed in Mathematics: \[ \text{Failed only in Mathematics} = \text{Failed in Mathematics} - \text{Failed in both} \] \[ = 42\% - 17\% = 25\% \] ### Step 4: Calculate the total percentage of candidates who failed in at least one subject Now, we can find the total percentage of candidates who failed in at least one subject by adding the percentages of those who failed only in Science, only in Mathematics, and those who failed in both: \[ \text{Total failed} = \text{Failed only in Science} + \text{Failed only in Mathematics} + \text{Failed in both} \] \[ = 35\% + 25\% + 17\% = 77\% \] ### Step 5: Calculate the percentage of candidates who passed in both subjects To find the percentage of candidates who passed in both subjects, we subtract the total percentage of candidates who failed from 100%: \[ \text{Passed in both} = 100\% - \text{Total failed} \] \[ = 100\% - 77\% = 23\% \] ### Final Answer Thus, the percentage of candidates who passed in both subjects is **23%**. ---
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