Zcos
Score Card
Quantitative Aptitude
Total Ques
Attempt
Correct
Score
Easy
24 Ques
0
0
24
Medium
196 Ques
0
2
194
Hard
30 Ques
0
0
30
General Instruction:
Test contains total 20 questions.
Time allowed to finish is 30 mins.
There is no negative marking.
Question - 1.
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
2.3 m
4.6 m
7.8 m
9.2 m
Solution:
Let AB be the wall and BC be the ladder.
Then, ACB = 60º and AC = 4.6 m.
AC/BC = cos 60º = 1/2
BC = 2 x AC
BC = 2 x 4.6
BC = 9.2 m
Question - 2.
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Rs. 8400
Rs. 11,900
Rs. 13,600
Rs. 14,700
Solution:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs.[35000 x (21/50)] = Rs.14700
Question - 3.
Find the next number.
32 49 83 151 287 559 ?
1118
979
1103
1120
Solution:
32 + 17 = 49
49 + 34 = 83
83 + 68 = 151
151 + 136 = 287
287 + 272 = 559
559 + 544 = 1103
Question - 4.
The average marks in English of a class of 24 students is 56. If the marks of three students were misread as 44, 45, and 61 in place of the actual marks 48, 59 and 67 respectively, then what would be the correct average ?
56.5
57
57.5
58
Solution:
Total marks = 24 x 56 = 1344
Total of actual marks = 1344 - (44 + 45 + 61) + (48 + 59 + 67) = 1368
Actual average = 1368/24 = 57
Question - 5.
From a well shuffled pack of 52 playing cards, one card is drawn at random. What is the probability that the card drawn will be a black king ?
1/26
7/13
3/52
1/13
Solution:
Total possible outcomes =
52
C
1
= 52
Favourable outcomes = 2
Required probability = 2/52 = 1/26
Question - 6.
In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together ?
720
1440
5040
3600
Solution:
Total number of letters is 7, and these letters can be arranged in 7! ways.
= 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040 ways.
There are seven word THERAPY including 2 vowels. (E, A) and five consonants.
Consider two vowels as one letter.
We have 6 letters which can be arranged in 6P6 = 6 ways.
But vowels can be arranged in 2! ways.
hence, the number of ways, all vowels will come together = 6! x 2!
= 1 x 2 x 3 x 4 x 5 x 6 x 2 = 1440
Total no. of ways in which vowels will never come together = 5040 - 1440 = 3600
Question - 7.
An article was purchased for Rs. 78350. Its price was marked up by 30%. it was sold at a discount of 20% on the marked up price. what was the profit percent on the cost price ?4%
5%
7%
4%
9%
Solution:
Cost price = Rs.78350
Marked price = 78350 x (130/100) = Rs.101855
Selling Price = 101855 x (80/100) = Rs.81484
Profit= 81484 - 78350 = 3134+Required profit % = (3134/78350) x 100 = 4%
Question - 8.
The simple interest accrued on a sum of a certain principal is 35,6727 in seven years at the rate 8 pcpa. What would be the contained interest accrued on that the principal at the rate of 2 pcpa in 2 years.
Rs. 2573.48
Rs. 2564.86
Rs. 2553
Rs. 2753.86
Solution:
Principal = (35672 x 100)/(7 x 8)= 63700
CI = 63700[1 + (2/100)]² - 63700
CI = Rs.2573.48
Question - 9.
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
1520 m²
2420 m²
2480 m²
2520 m²
Solution:
We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get:
l = 63 and b = 40
Area = (l x b) = (63 x 40) m² = 2520 m².
Question - 10.
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Rs. 3500
Rs. 3750
Rs. 3840
Rs. 3900
Solution:
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10X = 4Y or Y = (5/2)X
15X + 2Y = 4000
15X + 2x(5/2)X = 4000
20X = 4000
X = 200
So, Y = (5/2)x200 = 500
Hence, the cost of 12 chairs and 3 tables = 12X + 3Y
= Rs. (2400 + 1500)
= Rs. 3900
Question - 11.
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
2.91 m
3 m
3.8 m
4 m
Solution:
Area of the park = (60 x 40) m² = 2400 m².
Area of the lawn = 2109 m²
Area of the crossroads = (2400 - 2109) m² = 291 m²
Let the width of the road be X metres. Then,
60X + 40X - X² = 291
X² - 100X + 291 = 0
(X - 97)(X - 3) = 0
x = 3
Question - 12.
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
5 : 7 : 8
20 : 49 : 64
24 : 31 : 35
9 : 17 :25
Solution:
Let their investments be Rs. X for 14 months, Rs. Y for 8 months and Rs. Z for 7 months respectively.
Then, 14X : 8Y : 7Z = 5 : 7 : 8.
Now,14X/7Z = 5/8
98X = 40Y
Y = 49/20X
And, 14X/7Z = 5/8
112X = 35Z
Z = 112/35X = 16/5X
X : Y : Z = X : (49/20)X : (16/5)X
X : Y : Z = 20 : 49 : 64
Question - 13.
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
Rs. 6400
Rs. 6500
Rs. 7200
Rs. 7500
Solution:
Let the sum invested in Scheme A be Rs. X and that in Scheme B be Rs. (13900 - X).
Then, [(X x 14 x 2)/100] + [{(13900 - X) x 11 x 2}/100] = 3508
28X - 22X = 350800 - (13900 x 22)
6X = 45000
X = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
Question - 14.
A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
3/4
4/7
3/5
1/8
Solution:
Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14 = 4/7
Question - 15.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Rs. 305
Rs. 425
Rs. 475
Rs. 400
Solution:
C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1
C's share (for 3 days) = Rs.(3 x 1/24 x 3200) = Rs. 400.
Question - 16.
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
5/11
6/11
7/11
8/11
Solution:
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10)
Part filled by (A + B + C) in 3 minutes = 3 x (11/16) = 11/20.
Part filled by C in 3 minutes = 3/10
Required ratio = (3/10 x 20/11) = 6/11
Question - 17.
A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Rs. 120
Rs. 121
Rs. 122
Rs. 123
Solution:
Amount = Rs. [1600 x {1 + 5/(2 x 100)}²] + 1600 x {1 + 5/(2 x 100)}]
= Rs.[ 1600 x (41/40) x (41/40) + 1600 x 41/40]
= Rs. [ 1600 x 41/40{(41/40) + 1}]
= Rs. [(1600 x 41 x 81)/(40 x 40)] = Rs. 3321.
C.I. = Rs. (3321 - 3200) = Rs. 121
Question - 18.
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
1 : 3
3 : 2
3 : 4
4 : 5
Solution:
Let the speeds of the two trains be X m/sec and Y m/sec respectively.
Then, length of the first train = 27X metres,
and length of the second train = 17Y metres.
(27X + 17Y)/(X + Y) = 23
27X + 17Y = 23X + 23Y
4X = 6Y
X/Y = 3 : 2
Question - 19.
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
24 years
27 years
31 years
35 yars
Solution:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5X + 3)/(4X + 3) = 11/9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
Question - 20.
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Rs. 900
Rs. 1500
Rs. 2000
Rs. 2100
Solution:
Let the shares of A, B, C and D be Rs. 5X, Rs. 2X, Rs. 4X and Rs. 3X respectively.
Then, 4X - 3X = 1000
X = 1000
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
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