Question

In an examination the average marks of risha is 74.if she got 16 more matks in hindi and 20 marks in english then her average would have been 78.find the total number of subjects he studied?

Answer 1

Let total number of subjects be "M".

In a examination average marks of Risha is 74. She got 16 marks more in hindi ans 20 marks in english. Then the average of her marks become 78.

Average marks of Risha = Sum of her average marks, hindi and english marks/Total number of subjects.

→ (74M + 16 + 20)/M = 78

→ (74M + 36)/M = 78

→ 74M + 36 = 78M

→ 74M - 78M = - 36

→ - 4M = - 36

→ 4M = 36

→ M = 9

∴ She studied total 9 subjects.

________________________________

✯ Verification :

From above calculations we have M = 9

Put value of M in this : (74M + 16 + 20)/M = 78

→ [74(9) + 16 + 20)]/9 = 78

→ (666 + 36)/9 = 78

→ 702/9 = 78

→ 78 = 78

Answer 2

Answer:

${\bold{\therefore Number\:of\:subject\:she\:studied=9}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about an examination average marks is given.

• Condition: If she got 16 more marks in hindi and 20 marks in english her average marks would 78.

• We have to find the number of subjects she studied.

$\underline \bold{Given : } \\ \implies Average \: marks = 74 \\ \implies Let \: Number \: of \: subjects = x \\ \\ \underline \bold{To \: Find : } \\ \implies Number \: of \: subjects = ?$

• According to given question :

$\implies \frac{74x + 16 + 20}{x} = 78 \\ \bold{Cross \: multiply \: them : } \\ \implies 74x + 16 + 20 = 78x \\ \implies 74x - 78x = - 20 - 16 \\ \implies - 4x = - 36 \\ \implies x = \frac{ - 36}{ - 4} \\ \bold{\implies x = 9} \\ \\ \bold{\therefore She \: studied \: 9 \: subjects} \\ \\ \bold{ \huge{Verification : }} \\ \\ \implies \frac{74x + 16 + 20}{x} = 78 \\ \: \: \: \: \: \: \: \: \bold{Left \: hand \: side} \\ \implies \frac{74x + 16 + 20}{x} \\ \bold{Putting \: value \: of \: x} \\ \implies \frac{74 \times 9 + 16 + 20}{9} \\ \implies \frac{666 + 36}{9} \\ \implies \frac{702}{9} \\ \bold {\implies 78} \\ \: \: \: \: \: \: \bold { \therefore LHS = RHS} \\ \: \: \: \: \: \bold{\huge{Verified}}$