61. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price, The ratio of the cost price and the printed price of the book is:
(A) 45:56
(B) 45:51
(C) 47:56
(D) 47:51
Answer:
(A) 45:56
Explanation:
Let CP = 100. Selling Price to earn 12% = 112. Let Printed Price (PP) be x. A 10% discount means SP = 0.9x. So, 0.9x = 112, giving x = 1120/9. The ratio of CP to PP is 100 : (1120/9) = 900 : 1120 = 45 : 56.
62. Which of the following relationship is correct?
(A) A.M.≥G.M.≥H.M.
(B) H.M.≥G.M.≥A.M.
(C) G.M.≥A.M.≥H.M.
(D) A.M.≥H.M.≥G.M.
Answer:
(A) A.M.≥G.M.≥H.M.
Explanation:
In mathematics, the AM-GM-HM inequality states that for any set of non-negative real numbers, the Arithmetic Mean is greater than or equal to the Geometric Mean, which is greater than or equal to the Harmonic Mean.
63. P(A and B) is given by
(A) P(A)×P(B/A)
(B) P(A)×P(A)
(C) P(A)+P(A)
(D) P(A)+P(A)-P(A∩B)
Answer:
(A) P(A)×P(B/A)
Explanation:
By the general multiplication rule in probability, the joint probability P(A ∩ B) or P(A and B) equals P(A) * P(B|A).
64. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 80
(C) 100
(D) 200
Answer:
(C) 100
Explanation:
Equations: A – 10 = B + 10 (so A – B = 20), and A + 20 = 2(B – 20) (so A – 2B = -60). Subtracting the second from the first gives B = 80. Then A = B + 20 = 100.
65. A worker completes 5/8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
(A) 6
(B) 7
(C) 8
(D) 9
Answer:
(A) 6
Explanation:
Work left = 1 – 5/8 = 3/8. If 5/8 is done in 10 days, the rate is 1/8 per 2 days. To complete the remaining 3/8, it will take 3 * 2 = 6 days.
