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[WpProQuiz 7383]
Directions (1 – 5): Read the following passage carefully and answer the given questions.
I) In an institute X, there are four courses i.e. Engineering, Science, Arts and Commerce. Number of candidates enrolled in Science course is 1080 while that in Arts course is 880. The number of girls in Engineering course is 50% more than number of boys in Arts.
II) The number of boys in Commerce is 33.33% more than number of girls in Science. The ratio of number of boys to number of Girls in Commerce course is 4: 3.
III) There are (A) girls in Arts course which is half of number of boys in Science course which is half of number of girls in Engineering course. The ratio of number of boys in all courses to that of number of girls is (B): (C). Number of candidates enrolled in Commerce course is 25% of total candidates enrolled in all the courses together.
(NOTE: Total Candidates = Number of boys + Number of girls)
1) Which of the following is true as per the information provided in the passage?
a) A = 300; B>C
b) A= 240; B<C
c) A =300; B<C
d) A = 240; B>C
e) None of these
2) If there is another course of Management in which number of boys is 50% of number of girls in Science and total number of candidates in it are 25% less than number of total candidates in Arts. Number of girls in Management is D. Then
a) A > D
b) A < D
c) A ≥ D
d) A ≤ D
e) A = D
3) If in next year, there is an increase of 10% in number of boys in Engineering & Science both while number of girls remain same. What will be the ratio of number of boys in Engineering candidates to number of Science candidate in next year?
a) 149: 70
b) 298: 141
c) 296: 141
d) 99: 47
e) 74: 35
4) If there would be no course of Science but total candidates remain same such that all boys and girls are equally divided in all the three remaining courses. What would be the ratio number of boys in Engineering & Arts together to number of girls in Arts & Commerce together?
a) 57: 53
b) None of these
c) 2: 1
d) 55: 31
e) 56: 31
5) What is the percentage of number of boys in Science & Commerce together as compared to number of girls in Engineering & Arts together?
a) 106.67 %
b) 105 %
c) 110 %
d) 103.25 %
e) 107.5 %
Application Sums
6) Tinu, Rinu and Minu started the business with the investment of Rs.5000, Rs.8000 and Rs.6000 respectively. At the end of business the total profit is Rs.4500. If Tinu’s profit share is Rs.500 more than that of Minu’s profit share and Rinu’s profit share is Rs.1000 more that of Minu, then what is the ratio of the investment period of Tinu, Rinu and Minu?
a) 18: 15: 10
b) 12: 11: 9
c) 17: 13: 8
d) Cannot be determined
e) None of these
7) The selling price of Watch is Rs.920. The ratio of the marked price to cost price of the watch is 23: 20 and the ratio of the marked price to cost price of the Pen is 11: 10. If the ratio of the cost price of the watch to Pen is 2: 1 and the discount offers for watch is 20%, then what is the marked price of Pen?
a) Rs.550
b) Rs.650
c) Rs.450
d) Rs.350
e) None of these
8) Rahul invests Rs. x in scheme A which offers compound interest half yearly at 20% per annum for 2 years and he also invests the same amount in scheme B which offers compound interest at certain rate per annum for 2 years. If he received the total amount after 2 years from scheme A and B is equal, then find the rate offered by scheme B?
a) 19%
b) 20%
c) 21%
d) Cannot be determined
e) None of these
9) Ratio of the ages of A, B and C is 16: 8: 1 and after 8 years the ratio of the ages of A and C is 6: 1. If the product of the ages of B and D is 640 years and the difference between the ages of D and E is 16 years, then E is older than D, what is the average ages of E and C?
a) 18 years
b) 20 years
c) 24 years
d) 22 years
e) None of these
10) Ratio of the radius of the cone to circle is 1: 2 and the curved surface area of the cone is 396 cm2. If the circumference of the circle is 88 cm, then find the height of the cone?
a) 3√11 cm
b) 4√11 cm
c) 5√11 cm
d) 6√11 cm
e) None of these
Answers :
Directions  (1 – 5):
From I,
Number of Candidates in Science course = 1080
Number of candidates in Arts course = 880
Let number of boys in Arts course = a
Number of girls in Engineering course = a+50/100×a=1.5a
From II,
Let number of girls in Science course = 3b
Number of boys in Commerce course = 3b+33.33/100×3b=4b
Number of girls in Commerce course = ¾ ×4b=3b
From III,
Number of boys in Science course = ½ ×1.5a=0.75a
Number of girls in Arts course = ½ ×0.75a=0.375a
Now, 880=a+0.375a⟹a=640
1080=0.75a+3b⟹b=200
Total candidates in Commerce course = 4b+3b=7b=1400
Total candidates enrolled in all the courses together = 1400/25×100=5600
Total candidates in Engineering course = 5600-(1080+880+1400)=2240
Number of boys in Engineering course = 2240-1.5a=1280
1) Answer: d)
A = number of girls in Arts = 240
B/C = (total number of boys)/(total number of girls)
= (1280+480+640+800)/(960+600+240+600)=3200/2400=4∶3
A= 240; B>C
2) Answer: b)
Number of boys in Management course = 50/100×600=300
Total candidates in Management = 880-25/100×880=660
Number of girls in Management course = D=660 – 300=360
Clearly, A<D
3) Answer: c)
Number of candidates in Engineering in next year = 110/100×1280+960=2368
Number of candidates in Science in next year = 110/100×480+600=1128
Required ratio = 2368∶1128=296∶141
4) Answer: e)
Number of boys divided = 480/3=160
Number of girls divided = 600/3=200
Number of boys in Engineering & Arts together = 1280+160+640+160=2240
Number of girls in Arts & Commerce together = 240+200+600+200=1240
Required ratio = 2240∶1240=56∶31
5) Answer: a)
Number of boys in Science & Commerce together = 480+800=1280
Number of girls in Engineering & Arts together = 960 +240=1200
Required % = 1280/1200×100=106.67%
Directions (6-10) :
6) Answer: a)
Total profit = Rs.4500
Tinu – Minu = 500 ——– (1)
Rinu – Minu = 1000 —— (2)
Tinu + Minu + Rinu = 4500 —— (3)
500 + Minu + Minu + 1000 + Minu = 4500
3Minu = 3000
Minu = Rs.1000
Tinu = 1000 + 500 = Rs.1500
Rinu = 1000 + 1000 = Rs.2000
Required ratio = 1500/5000: 2000/8000: 1000/6000
= 3/10: 1/4: 1/6
= 18: 15: 10
7) Answer: a)
CP of Watch = 2x
CP of Pen = x
SP of Watch = 920
Marked price of Watch = 920/80 * 100 = 1150
CP of Watch = 1150/23 * 20 = Rs.1000
CP of Pen = 1000/2 = 500
Marked price of Pen = 500/10 * 11 = Rs.550
8) Answer: c)
Compound amount = P * (1 + R/100)n
x * (1 + 10/100)4 = x * (1 + R/100)2
114/104 = (1 + R/100)2
121/100 = 1 + R/100
121 = 100 + R
R = 21%
9) Answer: b)
(16x + 8)/(x + 8) = 6/1
6x + 48 = 16x + 8
10x = 40
x = 4
B’s age = 8 * 4 = 32 years
B * D = 640
D = 20 years
E = 20 + 16 = 36 years
C’s age = 4 years
Average = (36 + 4)/2 = 20 years
10) Answer: c)
Circumference of the circle = 2 * 22/7 * r
88 = 2 * 22/7 * r
r = 14 cm
Radius of the circle = 14 cm
Radius of the cone = 14 * ½ = 7 cm
CSA of the cone = πrl = 22/7 * r * l
396 = 22/7 * 7 * l
l = 18 cm
Height of the cone = √(182 – 72)
= 5√11 cm
