PE 1 - Percentage | Arithmetic - Percentage
The daily compensation of a laborer increase by 10% but the number of days worked by him per month drop by 10%. If he was originally getting Rs. 20,000 per month, what will he get per month now?
- (a)
Rs. 21,000
- (b)
Rs. 20,100
- (c)
Rs. 20,000
- (d)
Rs. 19,800
Answer: Option D
Explanation :
Let the daily compensation of the laborer be c.
Let number of days worked be d.
∴ Total earnings (e) = c × d = 20,000.
According to the conditions given, new earnings (e’) = 1.1c × 0.9d = 0.99 × cd = 0.99 × 20000 = Rs. 19,800.
Alternately,
Total earnings increases by 10% (due to compensation) and then reduces by 10% (due to number of days).
When a number is increased and then decreased by p% successively, overall % change = -p2/100%
∴ net change in salary = -1%
New salary = 20000(1 - 1%) = Rs. 19,800.
Hence, option (d).
Workspace:
When 10% is lost in grinding wheat, a country has to import 2 million tons; but when only 6% is lost. It has to import only 1 million ton. Find the quantity of wheat which grows in the country:
- (a)
24 million tons
- (b)
15 million tons
- (c)
20 million tons
- (d)
25 million tons
Answer: Option D
Explanation :
Let the wheat grown in the country be x million tons.
Consumption in the country = (Wheat produced – wheat lost) + Import
∴ Consumption initially = (w – 10% of w) + 2 = 0.9w + 2
∴ Consumption finally = (w – 6% of w) + 1 = 0.94 + 1
⇒ 0.9x + 2 = 0.94x + 1
⇒ 0.04x = 1
⇒ x =1/0.04= 25 million tons
Alternately,
Due to reduction in wastage from 10% to 6% (i.e., 4% reduction) the country imports 1 mn tons less.
⇒ 4% of wheat production = 1 mn tons
⇒ 4/100 × wheat production = 1 mn tons
⇒ wheat production = 100/4 = 25 mn tons.
Hence, option (d).
Workspace:
In an examination of 5 subjects, all with the same maximum marks, a candidate scores 60% aggregate marks and marks in individual subjects are in proportion to 3 : 3 : 4 : 5 : 5. What was the highest score in any subject?
- (a)
69%
- (b)
72%
- (c)
75%
- (d)
80%
Answer: Option C
Explanation :
Let highest marks in each subject be 100.
Then for 5 subjects max marks obtainable = 500.
Since the candidate has scored 60% in aggregate
⇒ 0.6 × 500 = 300 marks
It is also given that marks scored in five subjects are in the ratio 3 : 3 : 4 : 5 : 5.
Thus, maximum marks scored in any subject = 5/20 × 300 = 75 marks
Hence, option (c).
Workspace:
A salesman gets a flat commission of 5% on all sales and a bonus of 20% on all sales exceeding Rs. 1,00,000. If in a particular month he earns Rs. 55000, what were his sales worth?
- (a)
Rs. 3,00,000
- (b)
Rs. 2,25,000
- (c)
Rs. 2,30,000
- (d)
Rs. 2,50,000
Answer: Option A
Explanation :
Let the monthly sales be denoted by S
Then, by conditions in the problem, 0.05S + 0.2(S – 1,00,000)
⇒ 0.25S – 20,000 = 55,000
⇒ S = Rs. 3,00,000
Hence, option (a).
Workspace:
A shop’s receipts on the first day of the week were Rs. 10,000. On the second day 50% more than this, and on the third day 80% of the sum of the receipts of the first 2 days. What was the average of the receipts during this three day period (in rupees)?
- (a)
10533.33
- (b)
12300
- (c)
15000
- (d)
13500
Answer: Option C
Explanation :
Receipts on 1st day Rs. 10,000.
On 2nd day Rs. 1.5 × 10000 = 15,000
On 3rd day Rs. 0.8 × (10,000 + 15,000) = 20,000
∴ Average receipt would be (10000 + 15000 + 2000)/3 = Rs. 15000
Hence, option (c).
Workspace:
There are n questions in an exam. A student answered 3 of the first 4 questions correctly. Of the remaining questions he answered one-third correctly. All the questions have the same marks and there is no negative marking. If the student scored 50% marks, how many different values of n can be there?
- (a)
4
- (b)
3
- (c)
2
- (d)
None of these
Answer: Option D
Explanation :
To score 50% he must have answered 50% questions correctly.
From the conditions of the problem
3 + (n - 4)/3 = 0.5n
⇒ 9 + n – 4 = 1.5n
⇒ 0.5n = 5
⇒ n = 10 (i.e., only one value)
Hence, option (d).
Workspace:
A man in business loses in the first year 10% of his capital, but in the second year he gains 12% of what he had at the end of the first year and his capital is now Rs. 400 more than that at the beginning of first year. Find his original capital.
- (a)
Rs. 50,000
- (b)
Rs. 40,000
- (c)
Rs. 30,000
- (d)
None of these
Answer: Option A
Explanation :
Let c be the initial capital.
At the end of 1st year, capital remaining = 0.9c
At the end of 2nd year, capital remaining = 1.12 × 0.9c = 1.008c
It is further given that 1.008c = c + 400.
⇒ 0.008c = 400
⇒ c = 400/0.008 = Rs. 50,000
Hence, option (a).
Workspace:
A sum of money is to be divided among three sons in such a way that the first son gets 25% of the whole, the second 40% of the remainder and the third son the rest. If the 3rd son gets Rs. 1,500 more than the 2nd son, what would be the total sum divided?
- (a)
9,000
- (b)
10,000
- (c)
3,000
- (d)
None of these
Answer: Option B
Explanation :
Let x be the sum to be shared
1st son gets : 0.25x
Remaining amount = x - 0.25x = 0.75x
2nd son gets : 0.4 × 0.75x = 0.3x
3rd son gets : x – 0.25x – 0.3x = 0.45x
Now, third son gets Rs. 1,500 more than the 2nd son.
⇒ 0.45x – 0.3x = 1500
⇒ x = 10,000
∴ 1st son’s share = Rs. 2500
2nd son’s share = Rs. 3000
3rd son’s share = Rs. 4500
Hence, option (b).
Workspace:
In an examination Prakash secured 30% of the total marks and failed by 20 marks. Kashish secured 52% of the total marks and secured 24 marks more than minimum pass percentage. Find the pass percentage of marks.
- (a)
28%
- (b)
25%
- (c)
40%
- (d)
30%
Answer: Option C
Explanation :
Let total marks be x, and let pass marks be p.
Prakash: 0.3x = p – 20 …(1)
Kashish: 0.52x = p + 24 …(2)
(2) – (1)
⇒ 0.22x = 44
⇒ x = 200 and p = 80.
Pass % = 80/200 = 0.4 or 40%
Hence, option (c).
Workspace:
In an election 4% of the votes cast are invalid. A candidate gets 55% of the valid votes and wins the election by 480 votes. Find the total number of voters who voted (i.e., the number of votes cast). (There are only two candidates)
- (a)
5000
- (b)
5200
- (c)
4800
- (d)
None of these
Answer: Option A
Explanation :
Let the number of votes cast = v
∴ Valid votes = 0.96v
Winner gets 480 votes more than the other candidate.
⇒ 0.55 × 0.96v = 0.45 × 0.96v + 480
⇒ 0.096v = 480
⇒ v = 5000
Hence, option (a).
Workspace:
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