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There are 800 students in class X of a school. Out of them, 51% students passed in English, 48% students passed in Economic and 34% students passed in Hindi. 15% of students passed in English and Economics, 10% of students passed in English and Hindi and 13% of students passed in Economics and Hindi. Then, what is the number of students who are passed in all three subjects?

There are 800 students in class X of a school. Out of them, 51% students passed in English, 48% students passed in Economic and 34% students passed in Hindi. 15% of students passed in English and Economics, 10% of students passed in English and Hindi and 13% of students passed in Economics and Hindi. Then, what is the number of students who are passed in all three subjects? Correct Answer 40

GIVEN:

Total students in Class X = 800

Students passed in English = 51%

Students Passed in Economics = 34%

Students passed in Hindi = 34%

Students passed in English & Economics = 10%

Students passed in English & Hindi = 5%

Students passed in Economics & Hindi = 8%

CONCEPT:

Venn diagram.

CALCULATION:

Suppose, x% of students passed in all three subjects.

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Students who passed in only English & Economics = (15 – x) %

Students who passed in only English & Hindi = (10 – x) %

Students who passed in only Hindi & Economics = (13 – x) %

Students who passed in only English = (51 – 15 + x – 10 + x – x) % = (26 + x) %

Students who passed in only Hindi = (34 – 10 + x – 13 + x - x) % = (11 + x) %

Students who passed in only Economics = (48 – 15 + x – 13 + x – x) % = (20 + x) %

∴ Total number of students = 100%

⇒ (26 + x + 11 + x + 20 + x + 15 – x + 10 – x + 13 – x + x) = 100

⇒ 95 + x = 100

⇒ x = 100 – 95

⇒ x = 5%

Given, 100 % = 800

⇒ 1 % = 8

∴ 5% = 40

∴ Total number of students who passed in all three subjects is 40.

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