Question

Question 3:
In a class, there are 80 students and their average marks in the annual examination are 40. If the average marks of passed students are 60 and average marks of failed students are 35, then find out the number of students who failed. एक कक्षा में, 80 छात्र हैं और वार्षिक परीक्षा में उनके औसत अंक 40 होते हैं। यदि उत्तीर्ण छात्रों के औसत अंक 60 हैं और असफल छात्रों के औसत अंक 35 हैं, तो उन छात्रों की संख्या ज्ञात करें जो असफल रहे।​

Answer 1

AnswEr :

Let the Number of Failed Students be n.

Number of Passed Students be (80 - n).

• Average of Total Students = 40
• Average of Passed Students = 60
• Average of Failed Students = 35

• According to the Question Now :

⇒ Total Marks of Students = Total Marks of (Passed Students + Failed Students)

⇒ (Average × Numbers) = (Average × Numbers) + (Average × Numbers)

⇒ (40 × 80) = (60 × (80 - n)) + (35 × n)

⇒ 3200 = 4800 - 60n + 35n

⇒ 60n - 35n = 4800 - 3200

⇒ 25n = 1600

• Dividing both term by 25

⇒ n = 64

∴ Number of Failed Students will be 64.

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माना कि फेल छात्रों की संख्या n हैं

और उत्तीर्ण छात्रों की संख्या (80 - n) हैं

• कुल छात्रों का औसत = 40
• उत्तीर्ण छात्रों का औसत = 60
• असफल छात्रों का औसत = 35

• अब प्रश्न के अनुसार :

⇒ छात्रों के कुल अंक = (उत्तीर्ण छात्र + असफल छात्र) के कुल अंक

⇒ (औसत × संख्या) = (औसत × संख्या) + (औसत × संख्या)

⇒ (40 × 80) = (60 × (80 - n)) + (35 × n)

⇒ 3200 = 4800 - 60n + 35n

⇒ 60n - 35n = 4800 - 3200

⇒ 25n = 1600

• 25 द्वारा दोनों को विभाजित करना

⇒ n = 64

∴ फेल हुए छात्रों की संख्या 64 होगी।

#answerwithquality #BAL

Answer 2

Given :-----

• Total students = 80
• Average marks of all students = 40 .
• Average marks of passed students = 60
• Average marks of failed students = 35 .

To Find :-----

• Number of students who failed ...

we can solve it with Two Methods ..

First we will try basic Method ..

_________________________

Let Number of students failed were x .

Than passed students = (80-x) .

Now Sum of marks of all the students = Total Average × Total students = 80*40

→ Average marks of passed students = 60(80-x)

→ Average Marks of Failed students = 35*x

so,

According to Question Now ,,

→ 80*40 = 35x + 60(80-x)

→ 3200 = 35x + 4800 - 60x

→ 25x = 1600

Dividing 25 both sides we get,

→ x = 64 students ..

Hence, 64 students Failed in the Exam....

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Now, Lets Try to solve it without much Calculation,

we will Use Allegation Method :::----

→ Alligation is a rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.

We have Failed Average = 35

Passed Students Average = 60

and, Total Average = 40 (Mean) .

Using Alligation rule we get,,

35. 60

40

(60-40). : (40-35)

=. 20 : 5

or , 4 : 1

That Means , we have Total 4+1 = 5 units ..

Now,

→ 5 units (Total) ------------------- 80 students

→ 4 units (Failed) ------------------ 64 students ....

(Hence , Number of Failed Students were 64 ... )

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[ i can understand if alligation method is new for you, but if you practice this, you will save much time in Exam, and your Calculation will also be very easy .. We can use This method in Ratio and perportional Chapter, Mixture , Profit and loss, Simple interest , Average Etc.] [ if You Have any doubt , please Ask] .

(Hope it Helps you)

#BAL