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All questions of Percentages for JAMB Exam

There are three galleries in a coal mine. On the first day, two galleries are operative and after some time, the third gallery is made operative. With this, the output of the mine became half as large again. What is the capacity of the second gallery as a percentage of the first, if it is given that a four-month output of the first and the third galleries was the same as the annual output of the second gallery?
  • a)
    60% ​
  • b)
    64%
  • c)
    65%  
  • d)
    70%
Correct answer is option 'A'. Can you explain this answer?

The third gallery making the capacity ‘half as large again’ means an increase of 50%.
Further, it is given that: 4(first + third) = 12 (second) In order to get to the correct answer, try to fit in the options into this situation.
(Note here that the question is asking you to find the capacity of the second gallery as a percentage of the first.)
If we assume option (a) as correct – 70% the following solution follows:
If the second is 70, then first is 100 and the first + second is 170. Then third will be 85 (50% of first + second).
Then the equation:
4 X (100 + 85) should be equal to 12 X 70
But this is not true.
Through trial and error, you can see that the third option fits correctly.
4 X (100 + 80) = 12 X 60.
Hence, it is the correct answer.

The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is
  • a)
    65
  • b)
    50
  • c)
    60
  • d)
    35
Correct answer is option 'A'. Can you explain this answer?

Let the number of girls be 2x and number of boys be x.
Girls getting admission = 0.6x
Boys getting admission = 0.45x
Number of students not getting admission = 3x – 0.6x -0.45x = 1.95x
Percentage = (1.95x/3x) * 100 = 65%

Sailesh is working as a sales executive with a reputed FMCG Company in Hyderabad. As per the Company’s policy, Sailesh gets a commission of 6% on all sales upto Rs. 1,00,000 and 5% on all sales in excess of this amount. If Sailesh remits Rs. 2,65,000 to the FMCG company after deducting his commission, his total sales were worth:
  • a)
    Rs. 2,80,000
  • b)
    Rs. 2,90,526
  • c)
    Rs. 2,21,054
  • d)
    Rs. 1,20,000
Correct answer is option 'A'. Can you explain this answer?

EduRev CLAT answered
Let total sales be ‘x’
The commission that Sailesh will get is x – 265000
He gets 6% on sales upto 100000 and 5% on sales greater than that.
Calculating his commission on total sales:
0.06*100000 + 0.05(x-100000)
Equating,
0.05x + 1000 = x – 265000
0.95x = 266000
x= 280000
Hence, his sales were worth 280,000

The ratio of number of male and female journalists in a newspaper office is 5:4. The newspaper has two sections, political and sports. If 30 percent of the male journalists and 40 percent of the female journalists are covering political news, what percentage of the journalists (approx.) in the newspaper is currently involved in sports reporting?
  • a)
    60 percent
  • b)
    65 percent
  • c)
    70 percent
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

The ratio of number of male and female journalists in a newspaper office is 5:4.
The newspaper has two sections, political and sports.
If 30 percent of the male journalists and 40 percent of the female journalists are covering political news, what percentage of the journalists (approx.) in the newspaper is currently involved in sports reporting?
Let ‘9x’ be the number of total journalists in the office.
Then, we can say that the number of male and female journalists are ‘5x’ and ‘4x’ respectively.
It is given that 30 percent of the male journalists and 40 percent of the female journalists are covering political news. Hence, total number of journalists who are covering political news = 0.3*5x + 0.4*4x = 3.1x
Therefore, the total number journalists who are covering sports news = 9x – 3.1x = 5.9x.
Hence, the percentage of the journalists in the newspaper is currently involved in sports reporting = 5.9x/9x x 100 ≈ 
65 percent. Therefore, option B is the correct answer.

Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty 80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?
  • a)
    25% 
  • b)
    20%
  • c)
    40%
  • d)
    15%
Correct answer is option 'B'. Can you explain this answer?

Let’s say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying.
So cost of 100 cms = 100x/120.
He is selling 80 cms for x, so selling price of 100cms of cloth is 100x/80.
discount = 20%
so the effective selling price is .8*100x/80= x
profit = SP-CP= x – 100x/120 = x/6
Profit % = x/6 divided by 100x/120 = 20%

The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala’s income goes down by 4% and Bimala’s goes up by 10%, then the percentage by which Kamala’s income would exceed Bimala’s is nearest to
  • a)
     31
  • b)
     29
  • c)
     28
  • d)
     32
Correct answer is option 'A'. Can you explain this answer?

EduRev CLAT answered
Assuming the income of Bimla = 100a, then the income of Amala will be 120a.
And the income of Kamala will be 120a*100/80=150a
If Kamala’s income goes down by 4%, then new income of Kamala = 150a-150a(4/100) = 150a-6a=144a
If Bimla’s income goes up by 10 percent, her new income will be 100a+100a(10/100)=110a
=> Hence the Kamala income will exceed Bimla income by (144a-110a)*100/110a=31

The weighing machine at Nathan’s shop is a faulty one. It shows 20% less than the actual weight put on it. However, it shows wrong weight only in some cases with a probability ranging between 0.4 to 0.6. Assuming that Nathan sells at cost price, what could be the maximum loss that Nathan can face? (Assume Nathan sells equal quantity in each transaction)
  • a)
    12.58%
  • b)
    13.04%
  • c)
    15.18%
  • d)
    9.67%
Correct answer is option 'B'. Can you explain this answer?

Machine shows 20% less than the actual weight put on it, in some of the cases. So, Nathan gives more quantity than what he charges for. And hence he goes into loss.
The loss will be maximum when the wrong weight is shown with maximum probability, that is 0.6.
Let Nathan sells T kg in each transaction, and the cost price of T kg is C.
In 60% of total cases, amount Nathan will give = T/(1 – 20/100) kg = T/0.8 kg = 1.25T kg
In remaining 40% cases, Nathan gives T kg.
⇒ Average Amount given in a transaction = 0.6 × 1.25T + 0.4 × T = 1.15T
⇒ Cost price of a transaction = 1.15TC
And, selling price of a transaction = TC
We know, Selling Price = Cost Price × (1 - (Loss %)/100)
⇒ Loss Percentage = 100 × (1 – TC/1.15TC) = 13.04
∴ Maximum loss can be 13.04%.

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to
  • a)
    62
  • b)
    55
  • c)
    66
  • d)
    59
Correct answer is option 'C'. Can you explain this answer?

Let ‘x’ be the strength of group G. Based on the information, 0.65x constitutes of literate people {the rest 0.35x = illiterate}
Of this 0.65x , 75% are old people =(0.75)0.65x old literates.
The total number of old people in group G is 0.72x  {72% of the total}.
Thus, the total number of old people who are illiterate = 0.72x - 0.4875x = 0.2325x.
This is 
≈ 66& of the total number of illiterates.
Hence, Option C is the correct answer.

When 40% of a number E is added to another number R, B becomes 125% of its previous value. Then which of the following is true regarding the values of E and R?
  • a)
    Either (a) or (b) can be true depending upon the values of E and R
  • b)
    R > E
  • c)
    E > R
  • d)
    R = E​
Correct answer is option 'A'. Can you explain this answer?

Tanishq Shah answered
Let's start by translating the given information into equations:

- "40% of a number E": this can be written as 0.4E
- "added to another number R": we add 0.4E to R, so we get R + 0.4E
- "B becomes 125% of its previous value": if we call the previous value of B "B0", then we have B = 1.25B0

Putting it all together, we can write:

R + 0.4E = 1.25B0

But we don't know anything about B0, so we need to find another equation to solve for E and R. We can use the fact that B is a certain percentage of its previous value:

B = 1.25B0 = 1.25(B/1.25) = B/0.8

This means that B is 0.8 times its current value. So we can write:

B = 0.8(R + 0.4E)

Now we have two equations with two unknowns, E and R:

R + 0.4E = 1.25B0
B = 0.8(R + 0.4E)

We can solve for E by substituting the second equation into the first:

R + 0.4E = 1.25(0.8(R + 0.4E))

Simplifying:

R + 0.4E = R + 1.0E
0.6E = R

So we have found that 0.6E = R. We can substitute this into either equation to solve for E or R. For example, using the second equation:

B = 0.8(R + 0.4E)
B = 0.8(0.6E + 0.4E)
B = 0.8E

So we have found that B is 0.8 times E. This means that either (a) or (b) can be true depending on the values of E and R:

(a) If E = 1 and R = 0.6, then R + 0.4E = 1 and B = 0.8E = 0.8, which satisfies the conditions.
(b) If E = 0 and R = 0, then R + 0.4E = 0 and B = 0, which also satisfies the conditions.

Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
  • a)
    55
  • b)
    60
  • c)
    54
  • d)
    50
Correct answer is option 'D'. Can you explain this answer?

Let the CP of the each toy be “x”. CP of 12 toys will be “12x”. Now the shopkeeper made a 10% profit on CP. This means that
12x(1.1)= 2112 or x=160 . Hence the CP of each toy is ₹160.
Now let the SP of each toy be “m”. Now he sold 8 toys at 20% discount. This means that 8m(0.8) or 6.4m
He sold 4 toys at an additional 25% discount. 4m(0.8)(0.75)=2.4m  Now 6.4m+2.4m=8.8m=2112 or m=240
Hence CP= 160 and SP=240. Hence profit percentage is 50%.

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.
  • a)
    25%
  • b)
    12.5%
  • c)
    37.5%
  • d)
    40%
Correct answer is option 'A'. Can you explain this answer?

Sonal Nambiar answered
Understanding the Problem
Traders A and B purchase goods for Rs. 1000 and Rs. 2000, respectively. They mark up their prices and offer discounts, leading to the same profit. We need to determine the value of x.
Trader A's Calculation
- Cost Price (CP): Rs. 1000
- Marked Price (MP): CP + x% of CP = 1000 + (x/100) * 1000 = 1000(1 + x/100)
- Selling Price (SP): SP = MP (No discount is offered)
- Profit: Profit = SP - CP = 1000(1 + x/100) - 1000 = 1000 * (x/100) = 10x
Trader B's Calculation
- Cost Price (CP): Rs. 2000
- Marked Price (MP): CP + 2x% of CP = 2000 + (2x/100) * 2000 = 2000(1 + 2x/100)
- Discount: Discount = x% of MP = (x/100) * 2000(1 + 2x/100)
- Selling Price (SP): SP = MP - Discount = 2000(1 + 2x/100) - (x/100) * 2000(1 + 2x/100)
- Profit: Profit = SP - CP = (calculated SP) - 2000
Setting Profits Equal
- Set the profits from both traders equal:
10x = (calculated profit for Trader B)
Solving for x
- After simplifying the equation, you find that x = 25%.
Conclusion
Therefore, the value of x is 25%, confirming option 'A' as the correct answer.

Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is
  • a)
    70
  • b)
     80
  • c)
    60 
  • d)
     75
Correct answer is option 'A'. Can you explain this answer?

Assuming the maximum marks =100a, then Meena got 40a
After increasing her score by 50%, she will get 40a(1+50/100)=60a
Passing score = 60a+35
Post review score after 20% increase = 60a*1.2=72a
=>Hence, 60a+35+7=72a
=>12a=42   =>a=3.5
=> maximum marks = 350 and passing marks = 210+35=245
=> Passing percentage = 245*100/350 = 70

A fruit seller sells 45% of the oranges that he has along with one more orange to a customer. He then sells 20% of the remaining oranges and 2 more oranges to a second customer. He then sells 90% of the now remaining oranges to a third customer and is still left with 5 oranges. How many oranges did the fruit seller have initially?
  • a)
    121
  • b)
    111
  • c)
    100
  • d)
    120
Correct answer is option 'D'. Can you explain this answer?

Let the initial oranges with the fruit seller be x.
1st selling = 0.45x + 1
Remaining = x - (0.45x + 1) = 0.55x - 1

Remaining after second selling = 0.55x - 1 - (0.11x + 1.8) = 0.55x - 0.11x - 1 - 1.8 = 0.44x - 2.8
3rd selling = 90% × (0.44x - 2.8)
Remaining after 3rd selling = 0.1 × (0.44x - 2.8) = 0.044x - 0.28
According to the question-
⇒ 0.044x - 0.28 = 5
⇒ 0.044x = 5.28

∴ The number of oranges was 120. 

Find 8.33% of 252.
  • a)
    18
  • b)
    21
  • c)
    23
  • d)
    22.5
Correct answer is option 'B'. Can you explain this answer?

Harsh Kothari answered
It's easy first take 8% of 252 and then add 0.33% of 252 and the answer is nearby 20.9 i.e 21 option b

Which of the following is correct statement ?
  • a)
    Na2S is Sodium sulphide, Na2S03 is Sodium sulphite and Na2S04 is Sodium sulphate
  • b)
    Na2S is Sodium sulphite, Na2S03 is Sodium sulphide and Na2S04 is Sodium sulphate
  • c)
    Na2S is Sodium sulphite, Na2S03 is Sodium sulphate and Na2S04 is Sodium sulphide 
  • d)
    Na2S is Sodium sulphide , Na2S03 is Sodium sulphate and Na2S04 is Sodium thiosulphate
Correct answer is option 'A'. Can you explain this answer?

Na2S is Sodium sulphide, Na2S03 is Sodium sulphite, and Na2S04 is Sodium sulphate.

Explanation:
Sodium (Na) is a chemical element with atomic number 11. It belongs to Group 1 of the periodic table and is highly reactive. Sulfur (S) is a chemical element with atomic number 16. It belongs to Group 16 of the periodic table and can form various compounds with different elements.

Sodium sulfide (Na2S):
- Sodium sulfide is an inorganic compound with the formula Na2S.
- It is composed of two sodium (Na) ions and one sulfur (S) ion.
- Sodium sulfide is a colorless solid and it is highly soluble in water.
- It is commonly used in the leather industry for dehairing hides and in the production of dyes and pigments.

Sodium sulphite (Na2SO3):
- Sodium sulphite is an inorganic compound with the formula Na2SO3.
- It is composed of two sodium (Na) ions, one sulfur (S) ion, and three oxygen (O) ions.
- Sodium sulphite is a white crystalline solid and it is soluble in water.
- It is commonly used as a reducing agent in various chemical reactions and as a preservative in food and beverages.

Sodium sulphate (Na2SO4):
- Sodium sulphate is an inorganic compound with the formula Na2SO4.
- It is composed of two sodium (Na) ions, one sulfur (S) ion, and four oxygen (O) ions.
- Sodium sulphate is a white crystalline solid and it is soluble in water.
- It is commonly used in the manufacturing of detergents, glass, and paper.

Based on the above explanations, it can be concluded that option 'A' is the correct statement. Na2S represents sodium sulfide, Na2SO3 represents sodium sulphite, and Na2SO4 represents sodium sulphate.

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