Q1. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
- 15
- 16
- 18
- None of these
EXPLANATION
The correct option is 2.
Let C.P. of each article be Re1.
C.P of x articles = Rs.x and S.P of x articles =Rs.20.
Profit =Rs. (20−x).
∴20−x/x *100=25
⟹2000−100x=25x
⟹ 125 x = 2000
∴ x = 16
Q4. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
- 564
- 645
- 735
- 756
EXPLANATION
Option 4.
(7 men + 6 women) 5 persons are to be chosen for a committee.
Formula used: “C, = n!/(n – r)! r!
Calculation: Ways in which at least 3 men are selected;
3 men + 2 women
⇒ 4 men + 1 woman
⇒ 5 men + 0 woman
Number of ways = 7C3 × 6C2 + 7C4 × 6C1 + 7C5 × 6C0
7!/(3! x 4!) x 6!/(2! x 4!) + 7!/(4! x 3!) x 6!/(1! x 5!) + 7!/(5! x 2!) x 6!/(6!x 0!)
35 x 15+ 35 x 6 + 21
⇒ 735 + 21 = 756
The required no of ways = 756.
Q5. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
- 1/2
- 2/5
- 8/15
- 3/5
EXPLANATION
Option 3.
Here, S = {1, 2, 3, 4, …., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
