Question

3. In An examination 70 % passed in English 80 % passed in mathematics 10% failed in both the subjects If 144 candidates passed in both the subjects Find total number of
candidates
​

Answer 1

Given:

• In An examination 70 % passed in English 80 % passed in mathematics 10% failed in both the subjects and 144 candidates passed in both the subjects.

To Find:

• Find total number of candidates

Solution:

★ Here,

• 70% People passed English
• 80% People passed Maths
• 144 People passed both of them
• 10% Failed in both of them

★ Now,

➼ If 10% failed in both the subjects, so 90% either passed maths or english or both of them. so,

${ \purple{ \mapsto}} \tt \: students \: passed _{(only \: english)} = 90\% - 80\% \\ \\ { \purple{ \mapsto}} \tt \: students \: passed _{(only \: english)} = 10\% \: \: \: \: \: \: \: \: \: \: \: \: \:$

★ And,

${ \purple{ \mapsto}} \tt \: students \: passed _{(only \: math)} = 90\% - 70\% \\ \\ { \purple{ \mapsto}} \tt \: students \: passed _{(only \: math)} = 20\% \: \: \: \: \: \: \: \: \: \: \: \: \:$

★There by,

${ \purple{ \mapsto}} \tt \: students \: passed _{(both \: subjects)} = 90\% - (20\% + 10\%) \\ \\ { \purple{ \mapsto}} \tt \: students \: passed _{(both \: subjects)} = 90\% - 30\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \purple{ \mapsto}} \tt \: students \: passed _{(both \: subjects)} = 60\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

★ We know,

• No. of students passed both the subjects = 144
• Percentage of students passed both the subjects = 60%

 ✦ Let the total no.of students be x

★ So,

${ : \implies} \sf \: 60\% \: of \: x = 144 \\ \\ \\ { : \implies} \sf \frac{60}{100} \times x = 144 \\ \\ \\ { : \implies} \sf \frac{60x}{100} = 144 \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \frac{6x}{10} = 144 \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf x = \frac{144 \times 10}{6} \\ \\ \\ { : \implies} \sf x = 24 \times 10 \: \: \\ \\ \\ { : \implies} \sf { \purple{ \boxed{ \pmb{ \frak{x = 240}}} \bigstar}} \: \:$

Hence:

• 240 students applied for the examination

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Answer 2

Answer:

Failed candidates in English = (100 - 70) = 30%

Failed candidates in Mathematics = (100 - 80) = 20%

Percentage of passed students in both subject

= 100 -(20 + 10 + 10) = 60%

According to the question

60% of students = 144

Total students = 144/60 × 100 = 240

Step-by-step explanation:

Hope it helps..