Problem Solving

1) Peter got 30%, of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?

Possible AnswersSelected Possible Answer
A. 75

B. 250

C. 35

D. 85

E. 65

2) In an election contested by two parties, Party D secured12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?

Possible AnswersSelected Possible Answer
A. 24,000

B. 36,000

C. 168,000

D. 300,000

E. 20,000

3) A shepherd has 1 million sheep at the beginning of Year 2000. The numbers grow by x%(x>0) during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?

Possible AnswersSelected Possible Answer
A. y > x

B. x = y

C. x > y

D. x * y = 0

E. Cannot be determined

4) If the price of petrol increases by 25% and Kevin intends to spend only an additional 15% on petrol, by what percentage must he reduce the quantity of petrol purchased?

Possible AnswersSelected Possible Answer
A. 6.67%

B. 12%

C. 10%

D. 8%

E. 14%

5) A candidate who gets 20%marks fails by 11 marks but another candidate who gets 42% marks gets 22 marks more than the passing marks. Find the maximum marks.

Possible AnswersSelected Possible Answer
A. 150

B. 50

C. 100

D. 200

E. 250

6) A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

Possible AnswersSelected Possible Answer
A. 23

B. 17

C. 77

D. 29

E. None of these

7) 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?

Possible AnswersSelected Possible Answer
A. 70%

B. 15%

C. 80%

D. 20%

E. 90%

8) If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

Possible AnswersSelected Possible Answer
A. 20%

B. 16.67%

C. 25%

D. 33.33%

E. 30%

10% difference is 25 marks.

So 100% mark would be 250.

Pass mark would be (.3*250) + 10 = 85

1) Peter got 30%, of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?

Possible AnswersSelected Possible Answer
A. 75

B. 250

C. 35

D. 85

E. 65

romitvsingh wrote:
2) In an election contested by two parties, Party D secured12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?

Possible AnswersSelected Possible Answer
A. 24,000

B. 36,000

C. 168,000

D. 300,000

E. 20,000

(R+12) + R = 100%

R = 44% = 132000 Votes.
D = 56% = 168000

D-R = 36000 B

romitvsingh wrote:
3) A shepherd has 1 million sheep at the beginning of Year 2000. The numbers grow by x%(x>0) during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?

Possible AnswersSelected Possible Answer
A. y > x

B. x = y

C. x > y

D. x * y = 0

E. Cannot be determined

Say the number of sheep is 100 and x =10%, so after an year population becomes 110.
After famine pop. decreases by y% and becomes 100 again. (if it were to decrease by 10% again, the new pop would be 110-11 = 99,hence it decreases by a % less than 10)

Hence x>y C

romitvsingh wrote: 4) If the price of petrol increases by 25% and Kevin intends to spend only an additional 15% on petrol, by what percentage must he reduce the quantity of petrol purchased?

Possible AnswersSelected Possible Answer
A. 6.67%

B. 12%

C. 10%

D. 8%

E. 14%

Say cost of petrol is 100.
New cost = 125.
Now he spends only 115, so would get only 115/125 = 0.92 of the quantity.
SO he should reduce his consumption by 8% D

romitvsingh wrote:5) A candidate who gets 20%marks fails by 11 marks but another candidate who gets 42% marks gets 22 marks more than the passing marks. Find the maximum marks.

Possible AnswersSelected Possible Answer
A. 150

B. 50

C. 100

D. 200

E. 250

(42-20)% = 33 marks
22% = 33 marks
100% = 150 marks A

romitvsingh wrote: 6) A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

Possible AnswersSelected Possible Answer
A. 23

B. 17

C. 77

D. 29

E. None of these

Read the question wrong.. Edited post (Courtesy : Xeb)

Say the vendor has 200 apples

60% - 120 apples
15% of remainder - .15 * 80 = 12 thrown

68 remaining

50% - 34 Apples Sold
Remaining 34 apples thrown.

Total thrown = 12+34 = 46 = 23% A IMO

romitvsingh wrote:
7) 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?

Possible AnswersSelected Possible Answer
A. 70%

B. 15%

C. 80%

D. 20%

E. 90%

Given, 20% of all men play football and 20% of men above 50 play football.

80% of the men are less than or equal to 50 years old = 20% of total are above 50

20% 0f 20% Total = 4%
4% of men are above 50 and play football.

Therefore, 16% of the 20% who play football are below 50 = 16/20 * 100 = 80%

romitvsingh wrote:
8) If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

Possible AnswersSelected Possible Answer
A. 20%

B. 16.67%

C. 25%

D. 33.33%

E. 30%

Say cost of petrol is 100 and new cost is 125.

For 100 I would get only 100/125 (or) 4/5 of the quantity, so I should reduce 1/5th of my consumption or 20% A IMO.

P.S Kindly stick to 1 question per post.

shankar.ashwin wrote:

romitvsingh wrote:
2) In an election contested by two parties, Party D secured12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?

Possible AnswersSelected Possible Answer
A. 24,000

B. 36,000

C. 168,000

D. 300,000

E. 20,000

(R+12) + R = 100%

R = 44% = 132000 Votes.
D = 66% = 168000

D-R = 36000 B

Shankar ... how did you get D = 66% of the total? 44 + 66 = 110% ... am i missing something here?

factor26 wrote:

shankar.ashwin wrote:

romitvsingh wrote:
2) In an election contested by two parties, Party D secured12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?

Possible AnswersSelected Possible Answer
A. 24,000

B. 36,000

C. 168,000

D. 300,000

E. 20,000

(R+12) + R = 100%

R = 44% = 132000 Votes.
D = 66% = 168000

D-R = 36000 B

Shankar ... how did you get D = 66% of the total? 44 + 66 = 110% ... am i missing something here?

Sorry That was a typo, it is 56%.

(44/100) * x = 132000
x = 300000.
D = .56*300000 = 168000.

shankar.ashwin wrote:

romitvsingh wrote: 6) A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

Possible AnswersSelected Possible Answer
A. 23

B. 17

C. 77

D. 29

E. None of these

Say the vendor has 200 apples

60% - 120 apples
15% - 30 apples (thrown)

50 remaining

50% - 25 Apples Sold
Remaining 25 apples thrown.

Total thrown = 30+25 = 55 = 22.5% A IMO

You can get exact 23%:

Let's say of 200 apples (=100%)

on Day 1
he sold 60% = 120 apples
40% remaining = 80 apples

"He throws away 15 percent of the remainder" = 15% of 80 apples = 12 apples
68 apples remaining

on Day 2
he sold 50% of the remaining 68 apples = 34 apples
50% thrown away = 34 apples

34+12 apples = 46 apples were thrown away = [spoiler]23% A[/spoiler]

Where is the solution of question 1?

naimah wrote:Where is the solution of question 1?

It's the second post in the thread, but here's an alternative method.

Peter got 30%, of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?

Let's say that the maximum = m and that the passing grade = p.

Peter's 30% was 10 less than the passing grade, so .3m = p - 10

Paul's 40% was 15 more than the passing grade, so .4m = p + 15

We know that p = .3m + 10 and p = .4m - 15, so

.3m + 10 = .4m - 15, or

25 = .1m, or

250 = m

From there, .4m = p + 15, so .4*250 = p + 15, or 85 = p.