Percentage

# Percentage

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During an election 70% of the people who polled said that they would vote for Mr. X Of those who said that, only 60% actually voted for X. Out of those who did not say they would vote for Mr. X, 70% actually voted for X. What percent of those who polled did vote for X?

• a.66%
• b.42%
• c.74%
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A machine depriciates in value each year at the rate of 10 % of its previous value. However, every second year there is some maintainence work so that in that year, depreciation is only 5% of its previous value. If at the end of fourth year tha value of machine is 146205 then find the value of machine t the start of first year?

Hi Nancy!

let the value of the machine at the start of first year was A.

then according to question :  A x 90/100 x 95/100 x 90/100 x 95/100 = 146205

A = 146205 x 20/19 x 20/19 x 10/9 x 10/9

A = 200000.

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6% of budget of government is spent on education.if government increases its budget by Rs. 3000 crores and allocates the entire amount for education, the share of education jumps to 9 % what is the original government budget ? (is there shortcut for this question without equations)

6% of the budget + 3000 = 9% of ( budget + 3000)

6% of the budget + 3000 = 9% of budget + 9% of 3000

3% of budget = 2730

Hence , Budget = 2730 x 100/3 = 91000.

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Hi Samyak

Let the volumes of Cups A and B be 'x' and 'y' units respectively

After the replacements

Beaker A has y/10 - x/5 + 30 units of acid

Beaker B has x/5 - y/10 + 12 units of acid

Equating the above two equations, we get

2x - y = 90

x = y = 90 is the answer

Enjoy 🙂

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Pls give me solution to this

Ans given is B

Hello Kartikeya,

It is a poorly framed question. 37.6 seems wrong to me.

Sir i got the answer .. they are only considering the students who gave the exam. Thankyou for your reply.

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Equal number of males and females were asked, "Do you belebel in marriages are made in heaven?" Every person answered in either yes or no. 60% of those who said yes were males and 80% of those who said no were females. What %age of the females said yes?

Hello Richa ,

See the last example here ,  https://tathagat.mba/average-mixture/

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Let it be a square of side S.

Area = S²

Side S is increased by 20% so new side = 1.2S

New area = 1.44S

Percentage Increase = 44.

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Gopi went to fruit market with a certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes , then the number of oranges he can buy is?

Hello Nikita ,

Ratio of mangoes to oranges Gopi can buy is => 4 : 5

Originally he can buy 40 mangoes

After 10% of taxi fare he can buy : 40 x 90/100 = 36 mangoes .

He bought 20 mangoes so he has enough money left to buy 36 - 20 = 16 mangoes

So , 5/4 = Number of oranges /16

=> Number of orangess = 20

Alternate Approach :

Let the amount of money be  1oo

Cost of 1 mango => 100/50 = 2
cost of 1 orange => 100/40 = 2.5

After 10% of taxi fare money left : 90 .

cost of 20 mangoes => 40

Remaining amount : 90 - 40 = 50 .

So he can buy : 50/2.5 = 20 oranges

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First he will spend 10,000 in purchasing on which he will get 20% cashback which means he get 2000 RS. Nd again he will spend this money(2000) in purchasing nd he will get 20% cashback on 2000 RS. Which is 400 RS. And he will spend this also so total money for which he can buy products =10,000 + 2000 + 400

First he will spend 10,000 in purchasing on which he will get 20% cashback which means he get 2000 RS. Nd again he will spend this money(2000) in purchasing nd he will get 20% cashback on 2000 RS. Which is 400 RS. And he will spend this also so total money for which he can buy products =10,000 + 2000 + 400

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what is the sum of all the natural numbers frim 1-100 that are niether multiples of 2 nor a multiple of  5?

Hello Shubhra !

Remove all even numbers

we are left with 50 odd numbers: 1 + 3 + 5 + 7 +..... + 99 = 502 = 2500

(Sum of first n odd numbers = n2

Now remove all odd multiples of 5: (5 + 15 + ....+ 95) = 10 x (95+5)/2 = 500

Required Sum : 2500 - 500 = 2000.

Alternate Approach :

We can use Eulers Totient Function here ,

Sum of coprimes of N below N is = N x Phi(N)/2

So , 100 x Phi(100)/2 = 50 x 40 = 200.

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there is a rule in investment market they call it 72 rule

you divide the rate into 72 and you get the years in which sum will get double

here reverse of this rule will follow years is given so we divide years into 72 and we will get rate

72/6=12

option (a)

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what is the percentage change in perimeter if the length is increased by 20% and breadth is increased by 30%?

Let length =10  Width = 10

P= 40

Now length = 12 bredth = 13

P' = 50

So percentage increase =(10/40)*100= 25%

Let the original length of the rectangle be : L

Original Area: LB

Length is increased by 20% so new length : 120L/100 = 6L/5

Breadth is increased by 30% so new breadth : 130L/100 = 13L/10

New area : 6L/5 x 13B/10 = 78LB/50 = 39LB/25

% increase = (39-25)/25 x 100= 56%

Alternatively

Percentage increase will be the average of percentage increase in sides if perimeter is asked i.e (20+30)/2 = 25%

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where is the answer key of percentage assignment?

Check the notes section of TG's  facebook page.

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OUT OF TOTAL, 93.75% OF THE STUDENTS PASSED IN AN EXAMINATION. Find Minimum number of total students?

Let the total number of students be x.

So, 93.75% of x is an integer.

93.75% of x = 15/16 of x .

Smallest possible value of x  for which 15/16 of x is an integer is 16.

Hence minimum possible number of students = 16.

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A reduction of 20% in the price of eggs would enable a man to obtain 56 more for Rs. 10. what is the original price per dozen of eggs ?

20% reduction = 80% cost = 4/5 cost

so this would enable him to purchase 5/4 quantity  = 125% quantity = 25% more quantity

25% = 56

100% = 224 (at Rs 10)

hence intial price of 224 eggs is 10

per dozen cost = (10/224)*12 = 120/224 = 15/28

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