QuestionIn an exam, $58\%$ passed Hindi, $48\%$ passed English, and $17\%$ failed both. What percent passed both? Options: (a) $23\%$ (b) $17\%$ (c) $33\%$ (d) $18\%$ (e) None.

Studdy Solution

STEP 1

Assumptions1. The percentage of students who passed in Hindi is58% . The percentage of students who passed in English is48%
3. The percentage of students who failed in both the subjects is17%
4. We are looking for the percentage of students who passed in both the subjects

STEP 2

First, we need to find the total percentage of students who passed in either of the subjects. We can do this by adding the percentage of students who passed in Hindi and the percentage of students who passed in English.
$Total\, passed = Passed\, in\, Hindi + Passed\, in\, English$

STEP 3

Now, plug in the given values for the percentage of students who passed in Hindi and English to calculate the total percentage of students who passed.
$Total\, passed =58\% +48\%$

STEP 4

Calculate the total percentage of students who passed in either of the subjects.
$Total\, passed =58\% +48\% =106\%$

STEP 5

Now, we subtract the percentage of students who failed in both the subjects from the total percentage of students who passed. This will give us the percentage of students who passed in both the subjects.
$Passed\, in\, both = Total\, passed - Failed\, in\, both$

STEP 6

Plug in the values for the total percentage of students who passed and the percentage of students who failed in both the subjects to calculate the percentage of students who passed in both the subjects.
$Passed\, in\, both =106\% -17\%$

STEP 7

Calculate the percentage of students who passed in both the subjects.
$Passed\, in\, both =106\% -17\% =89\%$ However, this is not the final answer. This value represents the percentage of students who passed in at least one of the subjects, not necessarily both.

STEP 8

To find the percentage of students who passed in both subjects, we need to subtract the percentage of students who passed in only one subject from the total percentage of students who passed in at least one subject.The percentage of students who passed in only one subject is the sum of the percentages of students who passed in each subject minus twice the percentage of students who passed in both subjects (since we counted these students twice in the sum).
$Passed\, in\, both = Total\, passed -2 \times Passed\, in\, both$

STEP 9

Plug in the values for the total percentage of students who passed and the percentage of students who passed in both subjects to calculate the percentage of students who passed in both subjects.
$Passed\, in\, both =89\% -2 \times89\%$

STEP 10

Calculate the percentage of students who passed in both the subjects.
$Passed\, in\, both =89\% -2 \times89\% = -89\%$ This result is not possible, so there must be a mistake in our calculations.

STEP 11

Let's revisit our assumptions. We assumed that the percentage of students who passed in both subjects is the total percentage of students who passed minus the percentage of students who failed in both subjects. This is incorrect.
The correct formula to find the percentage of students who passed in both subjects is $Passed\, in\, both = Total\, passed -100\% + Failed\, in\, both$

STEP 12

Plug in the values for the total percentage of students who passed, the percentage of students who failed in both subjects, and100% to calculate the percentage of students who passed in both subjects.
$Passed\, in\, both =106\% -100\% +17\%$

STEP 13

Calculate the percentage of students who passed in both the subjects.
$Passed\, in\, both =106\% -100\% +17\% =23\%$ So, the percentage of students who passed in both the subjects is23%.
The correct answer is (a)23%.

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