Study the following given information and answer the question. (Q 1 – Q 5)

Average no. of Girls in St. Xavier college and Vijaya College is 210 & total number of boys in both the college is 810. Number of Girls is 2/3 of boys & number of Girls is 2/5 of number of Boys in St. Xavier college and in Vijaya College respectively.

Q1. Number of girls in Vijay college is what percent of the number of girls in St. Xavier College.

(a)  50%  (b) 62.5%  (c) 75% (d) 66 2/3% (e) 87.5%

Q2. Average number of girls in St. Xavier college and ‘X’ college is 320. If total number of students in ‘X’ college is 25% more than total number of students in St. Xavier college then find the number of boys in ‘X’ college.

(a)  450  (b) 400  (c) 375  (d) 350  (e) 300

Q3. Find the difference between the total number of students in Vijaya college to the total number of students in St. Xavier college.

(a)  15  (b) 20  (c) 25  (d) 30  (e) 35

Q4. Number of boys in Vijaya college is what percent more than number of boys in St. Xavier college?

(a)  32.5%  (b) 20%  (c) 50%  (d) 37.5%  (e) 25%

Q5. Ratio between number of boys in Vijaya college to number of boys in ‘Y’ college is 9 : 13 and number of girls in ‘Y’ college is 20% less than that in Vijaya college. Find the total number of students in ‘Y’ college?

(a)  784  (b) 794  (c) 789  (d) 798  (e) 778

Q6. A train is 216 m long. It crosses a platform in 19 seconds with speed 21 m/s. If some 21 m long boxes are added in train and it crosses same platform, then it takes 26 seconds to cross the platform at same speed. How many boxes were added to the train?

(a) 7           (b) 10             (c) 12             (d) 5   (e) 8

Q7.  A can complete a work in 36 days. B is 33.33% more efficient than A. In how many days both complete the work if they work on alternate days starting with A?

(a) 26 days          (b) 30 days (c) 28 days   (d) 31 days   (e) None of these

Q8. Sum of present ages of A and B is 41. Age of A 2 year hence is equal to age of C, 1 year ago. Age of A, 4 year hence is equal to age of B 1year ago and ratio of present age of A and D is 3 : 4. Find the difference of age of C and D.

(a) 3 years    (b) 5 years    (c) 6 years   (d) 4 years    (e) 8 years

Q9. In bag A there are 5 red balls, X green balls and 7 yellow balls. Probability of drawing one green ball from bag A is2/5. In bag B there are (X-3) red balls, (X-4) green balls and 6 yellow balls. 2 balls are drawn from bag B. Find the probability that both the balls are red colour?

(a) 2/23 (b) 3/21 (c) 4/21 (d) 2/21 (e) None of these

Q10.The average age of 28 men is 27 years. If the age of one more man is added to it, the average increases by 1 year. What is the age of the new man?

(a)  28 years (b) 42 years  (c) 56 years (d) 54 years  (e) None of these

Solution:

Q1-5 .  SOL (1- 5): Explanation

Total number of girls in St. Xavier college and Vijaya college = 210 × 2 =420
Let, Number of boys in St. Xavier college = x
And, Number of boys in Vijaya college = y
ATQ,
x + y = 810 …(i)
2/3x+2/5y=420…(ii)
On solving (i) & (ii)
x = 360, y = 450
Number of girls in St. Xavier college =2/3×360 =240
Number of girls in Vijaya college =2/5×450
= 180

SOL 1: C
Required%=180/240×100 =75%

SOL 2:  D
Girls in ‘X’ college = 2 × 320 – 240 = 400
Total no. of students in ‘X’ colleges =125/100×[360+240] = 750
Number of boys in ‘X’ college = 750 – 400 = 350

SOL 3: D
Required difference
= 450 + 180 – 360 – 240
= 630 – 600
= 30

SOL 4: B
Number of boys in ‘Y’ college =4509×13=650
Number of girls in ‘Y’ college =80100×180 = 144
Total number of students in ‘Y’ college = 650 + 144 = 794

SOL 5: E
Required%= (450 –360)/360×100 =25%

SOL 6: A
Length of platform = 21 × 19 – 216 = 183 m
216 + 183 + 21n = 21 × 26
21n = 147
n = 7

SOL 7: E
B will complete the work alone in  = ¾ * 36 = 27 days
A         36                  3
108
B          27                  4Let total units of work = 108No. of units done by A in 1 day = 3No. of units done by B in 1 day = 4Total work done in 2 days = 7 unitsWork done in 30 days = 7 × 15 = 105 units Remaining work will be done by A in = (108 – 105)/3 = 1 day

SOL 8: A
A + B = 41 …(i)
C -1 = A + 2
C = A + 3  and  A + 4 = B – 1 B = A + 5 …(ii)
From (i) + (ii)
A = 18 years
B = 18 + 5 = 23 years
C = 18 + 3 = 21 years
A/D = 3/4
D = 4 / 3 * 18 = 24
Required difference = 24 – 21 = 3 years

SOL 9 : D
Probability of drawing one green ball = X/(12+X) = 2/5
X = 8
Required probability = 5c2 / 15C2 = (5 * 4) /( 15 * 14 ) = 2 /21

SOL 10 : C
Age of New man = 28 + 28 = 56 yr.

Team AspirantsNotes.

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