Quantitative Aptitude Quiz Set-02

Quantitative Aptitude Quiz Set-02

 

 

 

Q1. Vijay purchased two different kinds of alcohol. In the first mixture the ratio of alcohol to water is 3 : 4 and in the second mixture it is 5 : 6. If he mixes the two given mixtures and makes a third mixture of 18 litres in which the ratio of alcohol to water is 4 : 5, the quantity of the first mixture (whose ratio is 3 : 4) that is required to make 18 litres of the third kind of mixture is
(1) 6 
(2) 7
(3) 8 
(4) 9
(5) None of these

Q2. Two casks of 48 litres and 42 litres are filled with mixtures of milk and water; the proportions in the two casks being respectively, 13 : 7 and 18 : 17. If the contents of the two casks be mixed, and 20 litres of water be added to the whole, what will be the proportion of milk and water in the resulting mixture ?
(1) 5 : 12 
(2) 7 : 13
(3) 12 : 13 
(4) 8 : 15
(5) None of these

Q3. Equal sums of money are deposited in two different banks by M/s Enterprise, one at compound interest, compounded annually and the other at simple interest, both at 5% per annum. If after two years, the difference in the amounts comes to Rs 200, what are the amounts deposited with each bank ?
(1) Rs 72000 
(2) Rs 64000
(3) Rs 80000 
(4) Rs 8400
(5) None of these

Q4. A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs 482 more if the interest was payable half yearly than if it was payable annually. The sum is
(1) Rs 10,000 
(2) Rs 20,000
(3) Rs 40,000 
(4) Rs 50,000
(5) None of these

Q5. What is the maximum percentage discount that a merchant can offer on her marked price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50% ?
(1) 16.67% 
(2) 20%
(3) 50% 
(4) 33.33%
(5) None of these

Q6. An article is listed at Rs 65. A customer bought this article for Rs 56.16 with two successive discounts of which one is 10%. The other discount of this discount scheme that was allowed by the shopkeeper is
(1) 4% 
(2) 3%
(3) 6% 
(4) 2.5%
(5) None of these

Q7. X and Y are partners in a business. X contributed 1/3 of the capital for 9 months and Y received 2/5 of the profits. For how long was Y’s money used in the business ?
(1) 4 months 
(2) 3 months
(3) 2 months 
(4) 5 months
(5) None of these

Q8. Two companies A and B quote for a tender. On the tender opening day, A realizes that the two quotes are in the ratio 7 : 4 and hence decreases its price during negotiations to make it Rs 1 lakh lower than B’s quoted price. B then realizes that the final quotes of the two were in the ratio 3 : 4. By how much did A decrease its price in order to win the bid ?
(1) Rs 7 lakhs 
(2) Rs 4 lakhs
(3) Rs 9 lakhs 
(4) None of these
(5) None of these

Q9. 40% of the students in a college play Basket ball, 34% of the students play Tennis and the number of students who play both the games is 234. The number of students who play neither Basket ball nor Tennis is 52%. Determine the student population in the college.
(1) 800 
(2) 1050
(3) 900 
(4) 850
(5) None of these

Q10. The capital of a company is made up of 50000 preferred shares with dividend of 20% and 20000 common shares, the par value of each type of share being Rs 10. The company had a total profit of Rs 180000 out of which Rs 30000 was kept in reserve fund and the remaining distributed to share-holders. Find the dividend per cent to the common shareholders.
(1) 20% 
(2) 35%
(3) 25% 
(4) 30%
(5) None of these

SOLUTIONS:

Q1 – Option (2)
Using Alligation method,
3/7                             5/11
                  4/9
5/11 – 4/9             4/9 – 3/7
= 1/99                      = 1/63
So, Ratio = 1/99 : 1/63 = 1/11 : 1/7 = 7 : 11
Required quantity = 7/18 x 18 = 7 ltrs

Q2 – Option (3)
In mixture A of 48 ltrs,
Milk = 13/20 x 48 = 156/5 ltrs
Water = 7/20 x 48 = 84/5 ltrs
In mixture B of 42 ltrs,
Milk = 18/35 x 42 = 108/5 ltrs
Water = 17/35 x 42 = 102/5 ltrs 
In final mixture,
Milk = 156/5 + 108/5 = 265/5 ltrs
Water = 84/5 + 102/5 = 186/5 ltrs
Required Ratio = 264/5 : 186/5 + 20 = 264 : 286 = 12 : 13

Q3 – Option (3)
Let P be the amount deposited in two different banks.
In 1st bank, 
CI = P (1 + 5/100)² – P = P (21/20)² – P
= 441P/400 – P = 41P/400
In 2nd bank,
SI = P x 5 x 2 / 100 = P/10
So, 41P/100 – P/100 = 200
=>P = Rs. 80000

Q4 – Option (2)
Let the sum be Rs. x
x(1 + 10/100)^4 – x(1 + 20/100)²
=> x[1.4641 – 1.44] = 482
=> x = 482/0.0241 = 20000

Q5 – Option (4)
Let cost price = Rs. 100
Marked Price = Rs. 150
Discount percent = 50/150 x 100 = 33.33%

Q6 – Option (1) 
Let the other discount be x%
65 x 90/100 x (100-x)/100 = 56.16
=> 100 – x = (56.16x100x100)/(65×90)
=> 100 – x = 96
=> x = 4%

Q7 – Option (2)
Ratio of capital of X and Y = 1/3 : 2/3 = 1 : 2
Let Y’s money was used for n months
(1 x 9) : (2 x n) = 3 : 2
=> n = 3months

Q8 – Option (2)
A quotes Rs. 7x initially
B quotes Rs. 4x initially
The new ratio changes to 3 : 4
Change is decrease of Rs. 4 lakhs

Q9 – Option (3) 
Let the number of students in college be 100.
Then, number of students who play both games = (34 + 40) – (48) = 26
If 26 plays both the games, then total number of students = 100
If 234 play both the games, then total number of students = 100/26 x 234 = 900

Q10 – Option (3) 
Dividend for preferred share of company = 50000 × 10 × 20/100 = Rs 100000
Rest dividend amount of company = 180000 – 100000 – 30000 = Rs 50000
Dividend per cent for common share = 50000×100/20000×10 = 25%