Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x 5x = (8 x 15) x=(8*15)/5=24
2. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A. 2 : 5 B. 3 : 7 C. 5 : 3 D. 7 : 3
Ans. C
Solution: Let 40% of A=2/3 B Then,40 A/100=2B/3 => 2A/5=2B/3 => A/B-[2/3 – 5/2]=5/3p A : B = 5 : 3.
3. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
A. 3 : 3 : 10 B. 10 : 11 : 20 C. 23:33:60 D. 32 :43:53
Ans. C
Solution:
Let A = 2k, B = 3k and C = 5k. A’s new salary = 115/ 100 of 2k =[115/ 100 x 2k]= 23k/ 10 B’s new salary = 110/ 100 of 3k = [110/ 100x 3k] = 33k/ 10 C’s new salary = 120/ 100 of 5k = [120/ 100 x 5k] = 6k New ratio = 23k : 33k : 6k = 23 : 33 : 60
4. 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?
A. 3/4 B. 4/7 C. 1/8 D. 3/7
Ans. B
Solution:
Let number of balls = (6 + 8) = 14. Number of white balls = 8. P (drawing a white ball)=8/14=4/7
5. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?
A. 1/13 B. 3/13 C. 1/4 D. 9/5
Ans. B
Solution:
Clearly, there are 52 cards, out of which there are 12 face cards. P (getting a face card)=12/52=3/13
6. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
A. 3 /20 B. 29/ 34 C. 47/ 100 D. 13 /102
Ans. D
Solution:
Let S be the sample space. Then, n(S) = 52C2 = 52 * 51/ (2*1)= 1326. Let E = event of getting 1 spade and 1 heart. n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = (13C1 x 13C1) = (13 x 13) = 169. P(E) =n (E)/n(S) = 169/ 1326= 13/102
7. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
A. 1/ 22 B. 3/ 22 C. 2/ 91 D. 2/ 81
Ans. C
Solution:
Let S be the sample space. Then, n(S)= number of ways of drawing 3 balls out of 15 = 15C3 = (15 x 14 x 13)/ (3 x 2 x 1) = 455. Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = (5 x 4)/ (2 x 1)= 10. P(E) = n(E) / n(S)= 10/ 455 = 2/ 91
8. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A. 1 /13 B. 2 /13 C. 1 /26 D. 1 /52
Ans. C
Solution:
Here, n(S) = 52. Let E = event of getting a queen of club or a king of heart. Then, n(E) = 2. P(E) =n(E)/ n(S)= 2/ 52= 1/ 26
9. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
A. 27 B. 33 C. 49 D. 55
Ans. B
Solution:
Let the numbers be 3x and 5x. Then ,(3x-9)/(5x-9)=12/13 23(3x – 9) = 12(5x – 9) 9x = 99 x = 11. The smaller number = (3 x 11) = 33.
10. In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
A. 50 B. 100 C. 150 D. 200
Ans. C
Solution:
Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively. Then, sum of their values=Rs[(25x/100)+(10*2x)/100+(5*3x)/100]=Rs 60x/100 60x/100=30 =>x=(30*100)/60=50 Hence, the number of 5 p coins = (3 x 50) = 150.
11. B2CD, _____, BCD4, B5CD, BC6D
A. B2C2D B. BC3D C. B2C3D D. BCD7
Ans. B
Solution:
Because the letters are the same, concentrate on the number series, which is a simple 2, 3, 4, 5, 6 series, and follows each letter in order.
12. DEF, DEF2, DE2F2, _____, D2E2F3
A. DEF3 B. D3EF3 C. D2E3F D. D2E2F2
Ans. D
Solution:
In this series, the letters remain the same: DEF. The subscript numbers follow this series: 111, 112, 122, 222, 223, 233, 333, …
13. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A. 3 B. 5 C. 7
D. Cannot be determined
Ans. C
Solution:
1 woman’s 1 day’s work=1/70 1 child’s 1 day’s work =1/140 (5 women + 10 children)’s day’s work =5/70 +10/140=1/14 +1/14=1/7 5 women and 10 children will complete the work in 7 days.
14. 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?
15. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
A. 380 B. 395 C. 400 D. 425
Ans. C
Solution:
Let the numbers be x and y. Then, xy = 9375 and x/y=15 Xy/(x/y)=9375/15 y2 = 625. y = 25. x = 15y = (15 x 25) = 375. Sum of the numbers = x + y = 375 + 25 = 400.
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