Quantitative Aptitude Practice Mixed Quiz – Set 23

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Quantitative Aptitude Practice Mixed Quiz – Set 23
1. The salary of Maria is Rs. 30000. She spends half of her salary in food, and one fifth of remaining salary on accommodation. Out of remaining, she spends one eighth on travel. Remaining amount goes to her savings. How much money does she save?
a)    Rs. 12000
b)    Rs. 15000
c)     Rs. 10500
d)    Rs. 9000
e)    Rs. 8800
2. An investor buys a total 360 shares of two stocks. The price of one stock is Rs. 2100 per share, while the price of the other stock is Rs. 2700 per share. The investor spends a total of Rs. 9, 00,000 how many shares of each stock did he buy? (Write number of 2100 Rs./share stock and 2700 Rs./share stock respectively)
a)    120 ; 240
b)    130 ; 260
c)     260 ; 130
d)    240 ; 120
e)    150 ; 300
3. There was one mess for 30 boarders in a certain hostel. On the number of boarders being increased by 10, the expenses of the mess were increased by Rs. 40 per month while the average expenditure per head diminished by Rs. 2. Find the original monthly expenses.
a)    Rs. 390
b)    Rs. 410
c)     Rs. 360
d)    Rs. 480
e)    Rs. 420
4. In a case, a detective has to find a secret code that is a ratio. Hint to that ratio is that is resulting ratio when among two numbers whose ratio is 4 : 5, first is increased by 20% and the second is decreased by 20%. Help the detective to find the ratio of the resulting numbers.
a)    4 : 5
b)    5 : 4
c)     5 : 6
d)    6 : 5
e)    5 : 3
5. A bag contains 50 paise, 25 paise and 5 paise coins. If these are in the ratio of 4 : 3 : 5, respectively and the total amount of money is Rs. 90, what is the number of 25 paise coins?
a)    90
b)    150
c)     100
d)    70
e)    40
6. A part of Rs. 38,800 is lent out at 6% per six months at simple interest. The rest of the amount is lent out at 5% per annum simple interest after one year. The ratio of interest after 3 years from the time when first amount was lent out is 5 : 4. Find the second part that was lent out at 5%.
a)    Rs. 26,600
b)    Rs. 28,800
c)     Rs. 27,500
d)    Rs. 28,000
e)    Rs. 37,800
7. The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs. 16. If the interest were compounded half yearly, the difference in two interests would be:
a)    Rs. 24.81
b)    Rs. 26.90
c)     Rs. 31.61
d)    Rs. 32.40
e)    Rs. 33.43
8. P bought an item for Rs. 800. He sold it to Q at 20% profit. Q sold it to R at 20% loss. Then, R sold it to S at 20% profit. Finally, S sold it to T at 20% loss. AT what price did T bought the item (in Rs.)?
a)    720
b)    728
c)     737.28
d)    756.28
e)    784.12
9. Pradeep invested Rs. 4000 for 7 months, Mahendra invested Rs. 5000 for 4 months and Harsh invested Rs. 6000 for 1 month, out of total profit of Rs. 5400, Harsh’s share would be
a)    Rs. 500
b)    Rs. 525
c)     Rs. 600
d)    Rs. 675
e)    Rs. 750
10. Anil, Bani and Chintu started a shop by investing Rs. 27,000 Rs. 81,000 and Rs. 72,000 respectively. At the end of the year the profile was distributed in the ratio of their investment. If Bani’s share of profit be Rs. 36,000 the total profit (in Rs.) was
a)    90,000
b)    85,000
c)     80,000
d)    75,000
e)    None of these
11. Ram and Shyam can complete a work in 15 days and 10 days respectively. They started doing work together but after 2 days Shyam had to leave and Ram alone completed the remaining work. The whole work was completed in?
a)    10 days
b)    8 days
c)     12 days
d)    15 days
e)    20 days
12. Two pipes can fill empty take separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute all the three pipes are open, empty tank becomes full in one hour. The capacity of the tank (in gallons) is
a)    800
b)    600
c)     500
d)    400
e)    300
13. A swimmer swims a distance of 36 km in 6 hours downstream and a distance of 40 km upstream in 8 hours. What is his speed in still water?
a)    5.5 k/h
b)    6 k/h
c)     7 k/h
d)    11 k/h
e)    None of these
14. Deepak purchased 2 kg of wheat at the rate of Rs.15 per kg and 3 kg of wheat at the rate of Rs.13 per kg. He sells the mixture to his friend, so at what price per kg he should sell the mixture in order to get a earn 33 1/3% profit on the cost price?
a)    Rs. 16.35
b)    Rs. 18.40
c)     Rs. 17.39
d)    Rs. 15.23
e)    Rs. 19.00
15. A box contains 5 green, 4 yellow 3 white marbles. Three marbles are drawn at random. What is the probability that they all are not of the same colour?
a)    3/44
b)    3/55
c)     52/55
d)    41/44
e)    None of these


Solutions:
1. C) Salary spent of food = Half of Rs. 30000 = Rs. 15000
Remaining money = Rs. 30000 – Rs. 15000 = Rs. 15000
Amount spent on accommodation = (1/5) × Rs. 15000 = Rs. 3000
Amount left = Rs. 15000 – Rs. 3000 = Rs. 12000
Amount spent on Travel = (1/8) × Rs. 12000 = Rs. 1500
Amount left that is to be spent on savings = Rs. 12000 Rs. 1500 = Rs. 10500

2. A) Let number of 2100 Rs. / share stock be x
Let number of 2700 Rs. / share stock be y
   X + y = 360    …..(i)
2100x + 2700y = 9,00,000
7x + 9y = 3000  ..(ii)
Multiplying equation (i) by 7 and subtracting from (ii), we get
2y = 3000 - 2520
2y = 480
y = 240
x = 360 240 = 120

3. C) Let initial expense be X and average be A.
Average expense = Total expense/Number of boarders
When there are 30 boarders, Expense, X = 30A ……………… (1)
Number of boarders increase by 10 and expense increases by Rs. 40 and average is decreased by 2.
X + 40 = (A - 2) × (30 + 10)
X + 40 = 40A - 80
Putting the value of X from equation (1), we get
30A + 40 = 40A - 80
10A = 120
A = 12
X = 30A = 30 × 12 = Rs. 360
Original monthly expenses = Rs. 360

4. D) Let the numbers are 4x and 5x
First is increased by 20%
Let a = 4x + 4x * 20/100 => a = 4x + (4x/5) = 24x/5
Similarly, let b = 5x – 5x * (20/100) => b = 4x
Therefore, new ratio is a : b = 24x/5 : 4x => a : b = 6 : 5

5. A) According to the given information,
Ratio of total coins = 4 : 3 : 5
Let’s assume the number of 50 paise coins = 4x, 25 paise coins = 3x and, 5 paise coins = 5x
Amount of money from 50 paise coins = 50×4x = 200x paise
Amount of money from 25 paise coins = 25×3x = 75x paise
Amount of money from 5 paise coins = 5×5x = 25x paise
Total money = Rs. 90 = 9000 paise
200x + 75x + 25x = 9000
300x = 9000
x = 9000/300 = 30
Number of 25 paise coins in the bag = 3x = 3 × 30 = 90
There are 90 coins of 25 paise in the bag

6. B) Let’s assume the Principal amount of first part to be Rs. x
the amount x is lent out at 6% per 6 months simple interest for 3 years.
% rate of interest per annum = 6 × 2 = 12%
Remaining amount = 38800 – x
the amount (38800 x) is lent out at 5% simple interest per annum for 2 years.
We know that, SI = PTR/100
=> SI on first part for 3 years = (x * 12 * 3)/100 = 0.36x
SI on second part for 2 years = [(38800 – x) * 5 * 2]/100 = 3880 – 0.1x
The ratio of Simple interests of first part to second part is 5:4
=> 0.36x/(3880 – 0.1x) = 5/4
1.44x = 19400 0.5x
1.94x = 19400
x = 10000
Principal Amount of second part = 38800 – 10000 = Rs. 28800

7. A) (C.I. on the principal for 2 years at 10%) - (S.I. on the principal for 2 years at 10%) = 16
Principal = Rs. (100 × 160)/(10 × 1) = Rs. 1600
Similarly, for 2 years compounded half yearly = Rs. (1600 × (1 + 5/100)4) = Rs. 1944.81
C.I. = Rs. (1944.81 1600) = Rs. 344.81
S.I. = Rs. (1600 × 10 × 2)/100 = Rs. 320
C.I. S.I. = Rs. (344.81 320) = Rs. 24.81

8. C) It is a case of successive selling.
We know, in a series of successive selling, the effective selling price will be given by
Selling price = Cost price × (1 ± Profit or Loss %1/100) × (1 ± Profit or Loss %2/100) × (1 ± Profit or Loss %3/100) ….
Selling price = 800 × (1 + 20/100) × (1 20/100) × (1 + 20/100) × (1 20/100)
Selling price = 800 × 1.2 × 0.8 × 1.2 × 0.8 = Rs. 737.28

9. C)
Partner
Money
Time (Months)
Amount
Pradeep
4000
7
28000
Mahendra
5000
4
20000
Harsh
6000
1
6000
Now profit shared by three partners would be in ratio of their amounts = 28000: 20000: 6000 = 14: 10: 3
Now Harsh’s share in profit would be
[3/(14 + 10 + 3)] * 5400 = 3/27 * 5400
3 × 200 = Rs. 600
Harshs share in profit is Rs. 600.

10. C) The profits shared by partners are always in the ratio of their investments (provided that all of them invested their money for equal time duration)
Hence, ratio of profits = 27000 : 81000 : 72000
=  3 : 9 : 8
Let profit of Anil, Bani and Chintu be 3x,9x and 8x.
 Then total profit will be = 20x.
Given that 9x = 36000
X = 4000
Total profit, i.e., 20x will be = 20 × 4000= 80,000

11. C) Ram completed a work in = 15 days
Work done by Ram in 1 day = 1/15
Shyam completed a work in = 10 days
work done by Shyam in 1 day = 1/10
Work done by Ram and Shyam together in 2 days = 2 * (1/15 + 1/10) = 1/3 part
Remaining work = 1- 1/3 = 2/3
Ram does the remaining 2/3 part in = 2/3 * 15/1 = 10 days

12. B) Let the time required by third pipe to empty the tank be T minutes
Part of the tank filled by first pipe in 1 minute = 1/24
Part of the tank filled by second pipe in 1 minute = 1/40
Part of the tank emptied by third pipe in 1 minute = 1/T
Part of the tank filled by all three pipes in 1 minute = 1/24 + 1/40 – 1/T
All three pipes can fill the tank in I hour or 60 minutes
Part of the tank filled by all three pipes in 1 minute = 1/60
1/24 + 1/40 – 1/T = 1/60
T = 20 minutes
Time required by third pipe to empty the tank = 20 minutes
Since, third pipe can empty 30 gallons of water per minute
The capacity of the tank (in gallons) = 20 × 30 =600 gallons

13. A) We know that
 Speed = (Distance/Time)
Let speed of swimmer in still water = a k/h and speed of stream = b k/h,
Speed of swimmer in downstream = a+b k/h
Speed of swimmer in upstream = a-b k/h
Then,
In downstream,
a + b = 36/6
a + b = 6  ---------[1]
Also, in upstream,
a – b = 40/8
a b = 5 ---------[2]
Solving equations [1] & [2]
We get,
a= 5.5 km/hr and b = 0.5 k/h.

14. B) We have mixture of 2 kg wheat at the rate of Rs.15 per kg and 3kg wheat at the rate of Rs.13 per kg.
Therefore, the weight of mixture = 2 + 3 = 5 kg
Total cost price of the mixture = (2 × 15) + (3 × 13) = 30 + 39 = Rs.69
Now cost price of the mixture per kg = 69/5 = Rs. 13.80
In order to gain 33 1/3% profit, SP = 13.8 + (33 1/3% of 13.8)
Selling price of one kg of mixture = 13.8 + 4.6 = Rs. 18.4
Hence, the selling price per kg = Rs. 18.4

15. D) Let s be the sample then 
n(s) =  no. of ways of drawing 3 marbles out of 12
12C3 = [(12 * 11 * 10)/(3 * 2 * 1)] = 220
Let ϵ be the event of drawing 3 balls of the same colour?
Then ϵ = n(ϵ) = (5C3 + 4C3 + 3C3) = (5C2 + 4C1 + 1)
= [(5 * 4)/(2 * 1)] + 4 + 1 = 15
P(ϵ) = n(ϵ)/n(s) = 15/220 = 3/44
Therefore Req. Probability = (1 – 3/44) = 41/44