Hello sir, Can you please explain this question

Rajiv is a student in a business school. After every test he calculates his cumulative average. QT and OB were his last two tests. 83 marks in QT increased his average by 2. 75 marks in OB further increased his average by 1. Reasoning is the next test, if he gets 51 in Reasoning, his average will be _____?

- 63
- 62
- 61
- 60

Hello Ritika,

Find the solution.........

Let initial average =a and number of subjects = n

According to first condition,

an + 83 = (n+1) (a + 2)

an + 83 = an + 2n + a + 2

a + 2n = 81…………………1)

According to second condition,

{(a + 2) (n + 1)+ 75} = (a+2+1)(n+2)

an + a +2n + 2 + 75 = an + 2a + 3n + 6

a + n =71 …………………………..2)

From eq. 1) and 2)

n = 10 and x = 61

After paper OT and OB

Average = 61 + 2 + 1 =64

Number of subjects = 10 + 1 + 1 =12

So after getting 51 in reasoning,

Average = (64 x 12 + 51)/(13) =819/13=63

Sir,

Please me with these two questions. I tried many times but not able to getting the answers.

**Q1.) A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is:-**

A)1 : 6 B)1 : 4 C) 1 : 5 D)1 : 7

**Q2.) The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is:-**

A)1 : 2

B)3 : 1

C)1 : 4

D)4 : 1

ANSWER 1

The concentration of sugar syrup in the mixture is 1/2. (The mixture has equal quantities of lemon juice and sugar syrup)

The concentration of sugar syrup in pure sugar syrup is 1.

The initial mixture and the pure sugar syrup are mixed in a ratio 1 : 3 to form a new mixture.

That is 2 items with sugar syrup concentrations 1/2 and 1 respectively are mixed in the ratio 1 : 3 to form a new mixture. So the concentration of sugar syrup in such a new mixture is

{(½)*1 + 1*3} / (1+3) = 3.5/4 = 7/8

The concentration of sugar syrup in the new mixture is 7/8, that means out of 8 units of volume of the new mixture, 7 units are sugar syrup and the remaining one unit is lemon juice.

Hence the ratio of lemon juice to sugar syrup in the new mixture is 1 : 7

ANSWER 2

Let there be ‘a’ number of students originally in the class and their average weight be ‘n’ kgs.

Let ‘b’ number of students join the class having an average weight of ‘n + 3’ kgs.

This excess weight of 3 kgs brought in by each new student is shared among all the students such that each of them increases by 0.6 kgs.

3b = 0.6(a + b)

3b = 0.6 a + 0.6 b

2.4b = 0.6a

a = 4b

a : b = 4 : 1

The ratio of the number of original students to the number of new students is 4 : 1

** Q1. **Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is ?

@neraj-naiyar Sir,

It is given that, a1, a2, a3,..... Ramesh, Gautham, ...., a22 writes an examination

Given that, Average score of the 21 students other than Gautham = 62

So, Total Score - Gautham's score = 62 x 21

Ramesh scored 82.5

It is given that, when Ramesh leaves, the average score drops down by 1 mark.

Which means that Ramesh scored more than the Overall class average.

Since his departure has resulted in the decrease of the overall class average by 1, his score is 21 more than the average.

Overall Class average = 82.5 - 21 = 61.5 marks

Total Score - Gautham's score = 62 x 21

61.5 x 22 - 62 x 21 = Gautham's score

1353 - 1302 = Gautham's score

Gautham's score = 51 marks.

Q1. Imagine that there are four hundred and fifty nine managers in a hotel. If the number of managers is enlarged by 36, the expenses of the food increased by Rs. eighty one per day while the average spending per head decreased by one. Find the original spending of the hotel on food?

a) 7344

b) 7244

c) 7044

d) 7444

the average of m students should be more than 40 to give total average more than 40 for maximum we will take m=5 and n=45, than

total avg =(40*40+45*5)/40+5

=1825/45

=40.5555

hence option 2 is correct

In June a football team played 60 games and won 30% of these. After a phenomenal winning streak , this team raised its average to 50% . How many games did the team win in a row to attain this average?

30% of 60 = 18 .

Let the team played n matches in a row .

so , ( 18 + n)/(60 + n ) = 1/2

n = 24 .

Hence,the team won 24 matches in a row .

In an office, there are n employees and their average age is 36 years. After two years, 5 employees whose average age is 40 years, leave the office and next after three years 5 employees whose average age is 30 years, joined the office. Now the average age of the employees of the office becomes 39.7 years. Find the number of employees in the office initially.

after two years average will become 38 then the total age of all employees =38n

5 people of age 40 leave then total age=38n-40*5 =38n-200

after 3 more years so then total age=(38n-200) +(n-5)3 [n-5 is because five employee have already left ]

then comes 5 people of age 30 then total age become =(38n-200) +(n-5)3 +30*5

now total people are still n and the average now is 39.7

{(38n-200) +(n-5)3 +150}/n =39.7

41n -200 +150-15 =39.7

1.3n=65

n=50

Hi Pulkit,

let the average height of 22 toddlers be 3x .

so the average height of two toddlers who left => x

Sum of the heights of 22 toddlers = 66x

Sum of the heights of remaining 20 toddlers = 66x - 2x = 64x

According to question ,

64x/20 - 66x/22 = 2

3.2x - 3x = 2

x = 10

hence the average height of the remaining toddlers = 3.2 x 10 = 32

a set of consecutive positive integers beginning with 1 is written on the blackboard .a student came along and erased one number.the average of the remaining numbers is 37(31/37).what was erased number?

The average is 37 31/37 = 1400/37

we know that average of 1st n consecutive number is (n+1)/2 but average is 35 31/37 hence

value of n should be close to 2 x 37= 74. If there are n numbers then after erasing we will have n-1 numbers then summation of the n-1 numbers = (n-1) x Avg = 1400(n-1)/37, hence n-1 should be divisible by 37, but n is close to 74 , hence n = 75 so that n-1 =74 is divisible by 37. Hence n = 75.

Sum of 1st 75 natural numbers = 75 x 76/2 = 2850

Sum of 74 number after erasing one number = 1400/37 x 74 = 2800

Hence the number that was erased = 2850 - 2800 =50 .

The average of the squares of First 'n' natural numbers starting from 1 is 130 . Then , what is the average of the cubes of these first n natural numbers ?

avg of square of first n natural nos is (n+1)(2n+1)/6=130

2n^2+3n+1=780

2n^2+3n-779=0

n=[-3+√(9+6232)]/2

n=38

sum of cube of first n natural nos. is ( **n** ( **n** +1)/2)^{2}^{ }

put value of n

38*39*38*39/4

avg=sum/n

=(38*39*38*39)/4*38

get answer

Swati has three cartons of books. The average price of the books in carton 1 was Rs 64, the average price of the books in Carton 2 was Rs 82 and the average price of the books in Carton 3 was Rs 95. The average price of all the books in Carton 1 and Carton 2 together was Rs 78 and the average price of all the books in Carton 2 and carton 3 together was Rs 90. What was the average price of the the books of three cartons?

A shipping clerk has five boxes of different but unknown weights. The clerk weighs the boxes in pairs. The weights obtained are 101, 102, 103, 104, 105, 106, 107, 108, 109, 111kg. What is the weight of the heaviest box?

Average of first n natural nos is (n+1)2=x

next n nos will be

n , n+1, n+2, n+3.......2n

their sum =n*n+ n(n+1)/2

average ={n*n+ n(n+1)/2}/n

average = n+x

hence option A

Sir , kindly share the solution to this question -

4! ( ^{4}C_{4} + ^{5}C_{4} + ^{6}C_{4} +...+^{14}C_{4})

Sum : 4! (^{15}C_{5}) = 72072

Average : 72072/11 = 6552