Quant Quiz

1. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

A: 2 : 3
B: 1 : 1
C: 3 : 4
D: 4 : 3
E: None of the above

2. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

A: 7600
B: 8020
C: 8400
D: Data Inadequate
E: None of the above

3. Simi went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

A: Rs. 15
B: Rs. 15.70
C: Rs. 19.75
D: Rs. 20
E: None of these

4. Abhishek was playing cricket and 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: 500/11%
C: 600/11%
D: 55%
E: 60%

5. 10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was

A: 25020
B: 33000
C: 35000
D: 40000
E: None of the above

6. 8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?

A: 4.2
B: 6.4
C: 6.8
D: 8
E: None of the above

7. Pragya spends 24% of her monthly income on food and 15% on the education of her children. Of the remaining salary, she spends 25% on entertainment and 20% on conveyance. She is now left with Rs. 10,736. What is the monthly salary of Pragya?

A: Rs. 27,600
B: Rs. 28,000
C: Rs. 31,200
D: Rs. 33,000
E: None of the above

Answers:

1-OPTION – D

sum of 5% of a and 4% of b = 5/100 * a + 4/100 * b
sum of 6% of A and 8% of B = 6/100 * a + 8/100 * b

NOW,
5/100 * a + 4/100 * b =2/3 (6/100 * a + 8/100 * b)
3(5/100 * a + 4/100 * b)= 2 (6/100 * a + 8/100 * b)
15a/100 + 12b/100 = 12a/100 + 16b/100
(15a+ 12b)/100 = (12a + 16b)/100
15a + 12b = 12a + 16b
15a – 12a = 16b – 12b
3a = 4b
a/b = 4/3
a:b = 4:3


2-OPTION – E

State A and State B had an equal number of candidates appeared.

In state A, candidates got selected = 6%
In state B, candidates got selected = 7%
Difference between the selected candidates from state A and B = 1%

This 1% is given which is equal to = 80

So, 100% will be equal to = 80*100 = 8000

Total appeared candidates in State A = total appeared candidates in State B = 8000

3-OTPION – E

Let the amount of taxable purchases be Rs.x.
Then, 6% of x = 30/100
6/100 * x = 30/100
x = (30/100×100/6) = 5.
Cost of tax free items = Rs.[25 – (5 + 0.30)]
= Rs. 19.70

4-OPTION – B

Number of runs made by running = 110 – (3 x 4 + 8 x 6) = 50.

Required percentage = 50/110 * 100 =500/11 %

5-OPTION – E

Let total voters = V
No. of voters who cast their vote = 0.9*V
Valid votes = 0.9*0.9*V = 0.81*V
Winner got 54% & loser got 46% i.e a difference of 8% or 0.08.

SO,
0.08 * (0.81*V) = 1620
V = 25000.


6-OPTION – C

Let the number of persons eligible to vote be x. Then,
Number of eligible persons between 18 and 21 = 8% of x.
Number of persons between 18 and 21, who voted = 85% of (8% of x)

85/100 * 8/100 * x = 68x/1000
Required percentage = 68x/1000 * 1/x * 100 = 6.8%


7-OPTION – E

Let the monthly salary of Pragya be Rs. ‘a’.
Then, [100-(25+20)]% of [100-(24+15)]% of a = 10736

55% of 61% of a = 10736 ————–> a = 32000