Quantitative Aptitude Practice Mix Questions – Set 25

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Quantitative Aptitude Practice Mix Questions – Set 25
1. 12 marbles are selected at random from a large collection of white, red, green and yellow marbles. The number of marbles of each colour is unlimited. Find the probability that the selection contains atleast one marble of each colour?
a) 34/91
b) 33/91
c) 36/91
d) 23/91
e) 37/91
2. Three persons Amar, Akbar and Anthony invested different amounts in a fixed deposit scheme for one year at the rate of 12% per annum and earned a total interest of Rs 3240 at the end of the year. If the amount invested by Akbar is Rs 5000 more than the amount invested by Amar and the invested by Anthony is Rs 2000 more than the amount invested by Akbar, what is the amount invested by Akbar?
a) Rs.12000
b) Rs.10000
c) Rs.8000
d) Rs.16000
e) Rs.11500
3. Two stations Lucknow and Bhadohi are 162 km apart. A train leaves from Lucknow for Bhadohi and simultaneously another train leaves from Bhadohi for Lucknow. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train starting from Bhadohi is:
a) 9 1/2km
b) 8 1/2km
c) 10 5/6km
d) 12 5/8km
e) 13 2/7km
4. A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs. 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for the 100 pens in order to earn a profit of 25%?
a) Rs.802.50
b) Rs.862.50
c) Rs.825
d) Rs.875
e) None of these
5. A construction company has 100/3% of its employees as women. 50% of these women are married and 100/3% of married women have children. 75% of the men are married and 200/3% of married men have children. If no two employees are married to each other what fraction of the employees do not have children?
a) 13/18
b) 11/18
c) 17/18
d) 7/18
e) None of these
6. The circumference of a circle is 20 cm more than the perimeter of the square. The ratio of the side of the square to the radius of the circle is 4 : 3. Find the ratio of the area of the square to the area of the circle.
a) 23 : 29
b) 45 : 51
c) 56 : 99
d) 51 : 61
e) None of these
7. Praveen, Ramu and Shashi entered into a partnership with capitals of Rs. 62000, Rs. 93000 and Rs. 124000 respectively. Praveen manages the business for a certain number of months while Ramu manages the business for the rest of the year. The person who manages the business get the total commission equal to 10% of the profits. If the total income of Praveen at the end of the year is Rs. 2900 and the total profit is Rs. 12000, for how many months did Praveen manage the business?
a) 3 months
b) 5 months
c) 8 months
d) 2 months
e) None of these
8. Anand goes to the market and buys a certain article at a certain price and sells it at 10% profit. Had his brother Srinath gone to the market, being a much better businessman, he would have purchased the article for 10% less and sold it for Rs 25 more than Anand sold at, thereby making a profit of 50% in the deal. What is Anand’s cost price?
a) Rs.120
b) Rs.110
c) Rs.100
d) Rs.90
e) None of these
9. A and B are two types of acid solutions containing water and acid in the ratios of 5 : 4 and 3 : 2 respectively, both by weight. What quantity of solution A, by weight, has to be mixed with 25 kg of acid solution B and 32 kg of acid so that the resultant mixture has 200/3% of acid content by weight in it?
a) 18kg
b) 20kg
c) 16kg
d) 17kg
e) None of these
10. Pintu in USA earns an annual income of $688.25 out of $10000 that he invested partly at 5% per annum and partly at 8% per annum simple interest. Ratio of money invested at 5% and 8%:
a) 149 : 251
b) 225 : 575
c) 545 : 105
d) 275 : 725
e) None of these


Solutions:
1. B) Let W, R, G, Y represents no. of white, red, green and yellow coloured marbles contained in the selection of 12 marbles.
No. of ways of selecting 12 marbles is equal to the no. of non-negative integral solutions of
W + R + G + Y  = 12
Total no. of ways = C (12 + 4 - 1, 4 - 1) = C (15 ,  3)
The no. of selections that contain at least one marble of each colour is equal to the number of positive integral solutions of W + R + G + Y = 12
= C (12 - 1, 4 - 1)  =  C (11 , 3)
Required Probability = C(11, 3)/C(15, 3) = 33/91

2. B) Let the amount invested by Amar be x
Amount invested by Akbar = x + 5000
Amount invested by Anthony = x + 7000
Now, According to the question,
Rate = 12%, Total Interest = Rs 3240
{x + (x + 5000) + (x + 7000)} × 12/100 = 3240
3x + 12000 = 324000/12 3x = 15000 x = 5000
Hence amount invested by Akbar = 5000 + 5000 = Rs 10000

3. A) Given the distance between Lucknow and Bhadohi = 162 km 
Let the speed of train starting from Bhadohi be x km/hour 
Then speed of train starting from Lucknow = x + 8 km/hour 
Distances travelled for 6 hours by trains starting from Lucknow and Bhadohi are 6(x + 8) and 6x km respectively. 
So, 162 = 6(x+8) + 6x  12x = 162 48  12x = 114  x = 9 1/km

4. B) Net Cost Price = CP + selling expenses = 1.15 × 600 = Rs 690 .
SP = Net CP + 25% of Net CP = 1.25 × 690 = Rs. 862.5

5. B) Let 90 be the no. employees in the company
Therefore, total women employees = 90/3 = 30
As no. of women married = 50% of 30 = 15
No. of married women having children = 100/3% of 15 = 5
No. of married women not having children = 15 – 5 = 10
Now, total male employees = total – no. of women = 90 – 30 = 60
75% of men are married = 75% of 60 = 45
No. of married men having children = 200/3% of 45 = 30
No. of married men not having children = 45 – 30 = 15
Now total married employees not having children in the company = no. of unmarried men and women + men and women not having children = 15 + 15 + 10 + 15 = 55
Required fraction = 55/90 = 11/18

6. C) Let radius of the circle = 3x, side of the square = 4x
According to the question,
2 π r = 4 × Side + 20 => 2 × 22/7 × 3x = 4 × 4x + 20 => 132x/7 – 16x = 20 => 20x = 140 => x = 7
Radius = 21cm, Side of the square = 28cm
Ratio of the area, = 28^2 : 22/7 × 21^2 = 56 : 99

7. B) Suppose Praveen manages the business for x months
So Ramu manages the business for (12 – x) months
Total profit = Rs. 12000
10% of 12000 is the total commission for those who manage the business = Rs.1200
Remaining profit = 12000 – 1200 = Rs. 10800
Remaining amount is divided among the three in the ratio equivalent to their investment which is given by,
Praveen : Ramu : Shashi = 62000 : 93000 : 124000 = 62 : 93 : 124
Praveen’s share in 10800  = [62/(62 + 93 + 124)] × 10800 = Rs.2400
But, Praveen's total share = Rs. 2900
Commission for Praveen for managing the business = 2900 – 2400 = 500 Rs
X = (500 × 12)/1200 = 5 months
Hence Praveen manages business for 5 months.

8. C) Let the cost price be Rs.x. Anand’s profit = 10%
=> SP of anand = (100 + 10)/(100 * x) = 1.1x
Now, as Srinath buys 10 % less than Anand
Srinaths cost price = (100 – 10)/(100 * x) = 0.9x
Selling Price of Srinath is Rs 25 more than that of Anand
Srinaths selling price = 1.1x + 25
Accotding to question,
Srinath’s profit = 50%
Profit% = Profit * 100/CP => SP – CP = Profit% * CP/100
1.1x + 25 – 0.9x = 50 * 0.9x/100 => 0.4x + 50 = 0.9x => 0.5x = 50 => x = 100
Hence cost price of Anand is Rs 100

9. A) Let the quantity of solution A be 9x
Water : Acid  in solution A = 5x : 4x
Acid = 4x kg
Weight of solution B = 25 kg Water : Acid  =  3 : 2
Acid in solution B = 10 kg
Additional 32 kg acid is also added
Now, Total acid = 200/3 % of total solution
4x + 10 + 32 = 2/3 (9x + 25 + 32)
=> 4x + 42 = 2 (3x + 19) => 2x = 4 => x = 2
Hence, quantity of solution A = 9 × 2 = 18 kg

10. A) Let money invested at 5% be $ x then money invested at 8% will be $ (10000 - x)
(x * 1 * 5)/100 + [(10000 – x) * 1 * 8]/100 = $688.25
5x – 8x + 80000 = 68825 3x = 11175 x = $3725
And money invested at 8% = $(10000 - 3725) = $6275
ratio of money invested = $3725 : $6275 = 149 : 251