Percentage question

Q1.Rita’s mathematics test had 75 problems i.e.10 arithmetic, 30 algebra and 35 geometry problems. Although she had answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly. She did not pass the test because she got less than 60% of the problems right. How many more questions she would have to answer correctly to earn 60% of the passing grade?

a) 2   

b) 6   

c) 5  

d) 7

e)  none of these.

Explanation

Answer : c

Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35) = (7 + 12 + 21) = 40
Questions to be answered correctly for 60% grade = 60% of 75 = 45.
Required number of questions = (45 – 40) = 5.

Q2. In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes.

a) 16800

b) 16000

c) 14680

d)16900

e)  none of these.

Explanation

Answer : a

Total number of the enrolled voters= x
x*3/4*49/50*3/4=9261=16800

Q3. 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 :
a) 2500
b) 2700
c) 2900
d) 3100
e)none of these

Explanation

Answer: b

Number of votes=100
Invalid votes=20%
First candidate got 55% of valid votes =55% of 80% =55/100* 80% =44%
Second candidate got votes =80%-44% =36% Total votes= 7500 36% of 7500= 2700

Q4.A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
a)  45%
b) 45⁵⁄_{11 %}
c) 54⁶⁄_{11 %}
d) 55%
e)none of these

Explanation

Answer: b

Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
Required percentage =(50 x 100/110)%=45 and 5/11%

Q5. 2025 sweets were distributed among the children in such way that the number of sweets received by each child is 20% of that of  total children.How many chocolate did each student can get if 20% of sweets are taken by each teacher.
a) 6
b) 10
c) 8
d) 9
e) none of these

Explanation

Answer: d

Let the total number of children be x
total number of chocolate taken by teacher=1*2025/5=405
x *(20% of x)=405
x²=405=9
Number of sweets received by each child = 20% of 45 = 9.

Q6. 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
a) 10000
b) 12000
c) 14000    
d) 16000
e)  none of these

Explanation

Answer : b

Q7. A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with ?
a) 6 %    
b) 8 %
c) 10 %    
d) 12 %
e)none of these

Explanation

Answer: b

Let the total income be x.
Then, income left = (100 -80)% of [100 - (35 + 25)] % of x = 20% of 40% of x = 20/100 * 40/100 * 100) % of x = 8 % of x.

Q8. A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:
a) Rs.180    
b) Rs.120
c) Rs.480    
d) data insufficient
e) none of these

Explanation

Answer: b

Q9. If the pice of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumpion of sugar by
a) 15    
b) 20
c) 25    
d) 30
e) none pf these

Explanation

Answer: b

Let original consumption = 100 kg and new consumption = x kg,
So, 100 * 6 = x * 7.50 => x = 80kg
Reduction in consumption = 20%.

Q10. If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction ?
a) 31/25    
b) 15/17
c) 14/25    
d) 11/16
e) none of these

Explanation

Answer: b