Percentage problems
- 1. The price of ghee is increased by 32%. Therefore, a family reduces its consumption, so that the increment in price of ghee is only 10%. If consumption of ghee is 10 kg before the increment, then What is the consumption now?
Options- A. 81/3 kg
- B. 83/4 kg
- C. 81/2 kg
- D. 9 kg Discuss
Correct Answer: 81/3 kg
Explanation:
Let price of ghee before increment = ? N
Consumption = 10 kg
Then, expenditure on ghee = ? 10N
After increment,
Expenditure on ghee = 110% of 10N = 11N
Price of ghee = 132% of N = (N x 132)/100 = 33N/25 per kg
? Now consumption = (11N x 25) / 33N kg
= 81/3 kg
- 2. The expenses on wheat, meat and vegetable of a family are in the ratio 12 : 17 : 3. The prices of these articles are increased by 20%, 30% and 50% respectively, The total expenses of the family on these articles are increased by?
Options- A. 231/3%
- B. 281/8%
- C. 271/8%
- D. 251/7% Discuss
Correct Answer: 281/8%
Explanation:
Let expenses on wheat be 12N.
Expenses on meat = 17N.
Expenses on vegetables = 3N.
? Total expenses = 32N.
Increased expenses = ? (120% of 12N) + (130% of 17N) + (150% of 3N)]
= ? [(120/100) x 12N] + [(130/100) x 17N] + [(150/100) x 3N]
= ? [72N/5 + 221N/10 + 9N/2]
= ? (144N + 221N + 45N)/10
= ? 410N/10
= ? 41
? Total increase percentage = (9N/32N) x 100 %
= 225/8 %
= 281/8%
- 3. In 1998, ratio of the numbers of students taking examinations in x and z states are respectively 3 : 5 : 6. Next year, the numbers of students are increased by 20%, 10% and 20% respectively. If ratio of the numbers of students in states x and z is 1 : 2, then find the number of students who sit to take examination in 1998.?
Options- A. 5000
- B. 6000
- C. 75000
- D. Data is insuffcient Discuss
Correct Answer: Data is insuffcient
Explanation:
In 1998
Let number of students in x = 3k
Number of students in y = 5k and
Number of students in z = 6k
Next year,
number of students in x = 3k + 20% of 3k = 18k/5
Number of students in y = 5k + 10% of 5k = 11k/2
Number of students in z = 6k + 20% of 6k = 36k/5
According to the question,
(18k/5) / (36k/5) = 1/2
Thus, data is insufficient.
- 4. The tank-full of petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full of petrol last?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
Correct Answer: 8
Explanation:
Let us assume that Arun uses N units of petrol everyday. so the amount of of petrol in the tank when it is full will be 10N. If he starts using 25% more petrol everyday. then the units of petrol he now use everyday will be
N(1 + 25/100) = 1.25N
So, the number of days his petrol will now last will be equal to (amount of petrol in tank) / (number of units used everyday)
= (10N) / (1.25N) = 10 / 1.25
= 8 days
- 5. In a examination out of 480 students, 85% of the girls and 70% of the boys passed. How many boys appeared in the examination, if total pass percentage was 75%?
Options- A. 370
- B. 340
- C. 320
- D. 360 Discuss
Correct Answer: 320
Explanation:
Total number of students = 480
percentage of total students passed = 75% of total student
= (75 x 480)/100 = 360 students
Now, using the condition from the question.
Let the number of boys be N
Then, 70% of N + 85% of (480 - N) = 360
? [(70 x N)/100] + [85 x (480 - N)]/100 = 360
? 70N - 85N + 40800 = 36000
? 40800 - 36000 = 85N - 70N
? 4800 = 15N
? N = 4800/15 = 320
? There are 320 boys who appeared for the examination,
- 6. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
Options- A. 2500
- B. 2700
- C. 2900
- D. 3100 Discuss
Correct Answer: 2700
Explanation:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = 7500*(80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes x (45/100)
7500*(80/100)*(45/100) = 2700
- 7. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?
Options- A. 20
- B. 30
- C. 40
- D. 50 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 40
Explanation:
The fruit content in both the fresh fruit and dry fruit is the same.
Given, fresh fruit has 68% water.so remaining 32% is fruit content. weight of fresh fruits is 100kg
Dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.
Fruit % in freshfruit = Fruit% in dryfruit
Therefore, (32/100) x 100 = (80/100 ) x y
we get, y = 40 kg.
- 8. If 20% of a = b, then b% of 20 is the same as :
Options- A. 4% of a
- B. 6% of a
- C. 8% of a
- D. 10% of a Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 4% of a
Explanation:
20% of a = b
=> (20/100) * a = b
b% of 20 =(b/100) x 20 = [(20a/100) / 100] x 20= 4a/100 = 4% of a.
- 9. The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
Options- A. 10000
- B. 12000
- C. 14000
- D. 16000 Discuss
Correct Answer: 12000
Explanation:
Purchase price = = Rs. [8748 * (10/9) * (10/9 )* (10/9)] = Rs.12000
- 10. A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?
Options- A. 54 %
- B. 64 %
- C. 74 %
- D. 84 % Discuss
Correct Answer: 64 %
Explanation:
Let the number be x.
Then, ideally he should have multiplied by x by 5/3. Hence Correct result was x * (5/3)= 5x/3.
By mistake he multiplied x by 3/5 . Hence the result with error = 3x/5
Then, error = (5x/3 - 3x/5) = 16x/15
Error % = (error/True vaue) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64 %
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