Mu Sigma Ratio’s Quiz-1

Let the person gets a salary x per month.

=> x/2 --Household expenses

=> x/4 -- Rent

=> x/5 -- Travel expenses

=> y= Rest amount deposited in bank = 50/-

There fore, x=x/2+x/4+x/5+y => x=(10x+5x+4x)/20 + 50

=> x=19x/20 + 50

=>x=1000;

Let number of boys be 300.
Number of girls = 200

Boys holding scholarship = (20/100) x 300 = 60
Girls holding scholarship = (25/100) x 200 = 50

Total student holding scholarship = 60 + 50 = 110
∴ Percentage of students not holding scholarship = [(500 -110) / 500] x 100%
= (390/500) x 100 %
= 78%

In 28 minutes Pipe B Can Fill tank = 1

∴ In 1 minute Pipe B Can Fill tank = (1/28)

3/4 of the tank is filled in time = (3/4) ÷ (1/28) = 21 minutes

After 21 minutes The tank remaining empty = 1 - (3/4) = (1/4)

∵ In 30 minutes Pipe A Can Fill tank = 1

∴ In 1 minute Pipe A Can Fill tank = (1/30)

In 1 minute Pipe A + Pipe B can fill tank = (1/30) + (1/28) = (29/420) ................ (LCM of 28, 30 = 420)

∵ (29/420)th of Tank can be filled by Pipe A & Pipe B combined in time = 1 mins

∴ 1 Tank can be filled by Pipe A & Pipe B combined in time = 1 ÷ (29/420) mins

∴ (1/4) Tank can be filled by Pipe A & Pipe B combined in time = (1/4) ÷ (29/420) mins

= (420/116) = (105/29) = 3.62 Minutes

Given that ratio of students to teachers in a school = 30 : 1

Let the number of students in the school = x

Number of teachers in the school = y

⇒ x/y = 30/1

⇒ x = 30y ------ ---------------------->1

Now 50 number of students are increased so, total number of students = x + 50

And 5 number of teachers are increased so, total number of teachers = y +5

Now the ratio of students to teachers = 25 : 1

⇒ (x + 50)/(y + 5) = 25/1

⇒ x + 50 = 25 × (y +5) ------ ---------------------->2

Substitute equation 1 in equation 2

⇒ 30y + 50 = 25y + 125

⇒ 5y = 75

⇒ y =15

∴ number of teachers at present = y =15

Video solution:

Let us take the cost of material, labor and maintenance cost as 4m, 6m and 7m respectively.

Hence, we have total cost = 4m + 6m + 7m = 17m

Hence, we have 4m = 10000

⇒ m = 10000/4 = 2500

Then we have total cost = 2500 × 17 = 42500

Total marks he secured=800*55/100=440
then,in English he got 15% of his secured marks=440*15/100=66

Let the age of teacher is \'a\' months.
average age of a class of 39 students is 15 years i.e. = 15 x 12 = 180 months.
Now average age of a class of 39 students plus teacher age become 180 + 3 = 183 months.
∴ 180 x 39 + a = 183 x 40
⇒ a = 300 months
⇒ Age of Teacher is 300/12 = 25 year

Let B\'s capital be Rs. x.
Then, (3500 x 12)/7x = 2/3
14x = 126000

x = 9000.

Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

Let their initial investments be 6x, 2x and 3x respectively.

A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.

B\'s share = Rs. (378 * 8/21) = Rs. 144.

Let the total share be x.
thn, according to ques,
A\'s share=x/3
B\'s share=x/2
remaining=x-(x/3+x/2)=x/6
Ratio of A,B,C= (2:3:1)
hence,
Share of A= (2/6)*4800=1600