IBPS Clerk Prelims: Quants Day 23

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Directions (1-5): Study the pie chart below which gives the distribution of the number of students in different sections of class 10 in a school. Answer the questions that follow.

1. Which of the following combination of sections contribute to 50% of the total strength of class 10?
   A) A, B, F
   B) B, C, F
   C) A, B, C
   D) C, D, E
   E) None of these
   
   Answer & Explanation

   C) A, B, C
   Explanation:
   A, B, F = 36^o+72^o+18^o = 126^o
   B, C, F = 72^o+72^o+18^o = 162^o
   A, B, C = 36^o+72^o+72^o = 180^o
   C, D, E = 72^o+18^o+45^o = 135^o
   180^o is the half of complete 360^o, so sections A, B, and C contribute to 50% of total strength.
   
   
   
2. If there are 144 students in section A, then what is the number of students in section G?
   A) 396
   B) 108
   C) 325
   D) 366
   E) None of these
   
   Answer & Explanation

   A) 396
   Explanation:
   Let total number of students in class 10 is x
   So (36/360) * x = 144
   This gives x = 1440
   So number of students in section G = (99/360) * 1440 = 396
   
   
3. If the number of students in section B is 50% more than that in section A, then number of students in section A is what percent less than that in section B?
   A) 16 2/3%
   B) 25%
   C) 33 1/3%
   D) 40%
   E) 50%
   
   Answer & Explanation

   C) 33 1/3%
   Explanation:
   There is no need to see the pie chart to answer this question
   Required % = 50/(100+50) * 100
   
   
4. Find the number of students in sections A, B and E together.
   A) 644
   B) 524
   C) 500
   D) Cannot be determined
   E) None of these
   
   Answer & Explanation

   D) Cannot be determined
   Explanation:
   Number of students in section A = 36/360 * (total number of students in class 10)
   Since we are not given the total number of students in class 10, we cannot determine the number of students in each section.
   
   
5. If the total number of students of class 10 increase by 50% and students in section A increase by 20%, then what will be the angle for section A in the new pie-chart?
   A) 35.8^o
   B) 25.5^o
   C) 36.4^o
   D) 28.8^o
   E) None of these
   
   Answer & Explanation

   D) 28.8^o
   Explanation:
   Let total students in class 10 is ‘s’. After increase by 50%, new number of students = 150/100 * s = 3s/2
   Angle for section A is 36^o, so students in section A = 36/360 * s = s/10. They increase by 20%, so new number of students in section A = 120/100 * s/10 = 6s/50
   So new angle for A = [(6s/50)/(3s/2)] * 360 = 28.8^o
   
   
6. A jar contains 4 green balls, 4 white balls and 4 yellow balls. If 3 balls are drawn at random, find the probability that the balls are not of the same color.
   A) 44/57
   B) 52/55
   C) 3/55
   D) 10/31
   E) None of these
   
   Answer & Explanation

   B) 52/55
   Explanation:
   The probability can be found by subtracting prob. that all balls are same in color from 1.
   Total ways of drawing 3 balls out of total 12 balls = ¹²C₃ = 220
   Case 1: all balls green
   Ways are ⁴C₃ = 4
   Case 2: all balls white
   Ways are ⁴C₃ = 4
   Case 3: all balls yellow
   Ways are ⁴C₃ = 4
   So prob. that all balls are of same color = (4+4+4)/220 = 12/220 = 3/55
   Prob. that they are not of same color = 1 – 3/55 = 52/55
   
   
   
7. A, B and C start a business in which A’s contribution is 3/2 times that of B’s and also A’s contribution is thrice that of C’s. Their total investment in the business is Rs 15,000. Find the share of B in the profit of Rs 3000 at the end of a year.
   A) Rs 2,000
   B) Rs 1,500
   C) Rs 1,050
   D) Rs 1,000
   E) Rs 500
   
   Answer & Explanation

   D) Rs 1,000
   Explanation:
   Let A’s contribution = Rs x, then B’s contribution = 2/3 * x and C’s contribution = 1/3 * x
   Then profits in the ratio –
   A : B : C = x : 2x/3 : x/3 = 3 : 2 : 1
   So share of B = [2/(3+2+1)] * 3000 = 1000
   
   
8. A, B and C together can complete a piece of work in 4 days. All started the work and after working for 2 days, B left. A and C completed the remaining work in 3 days. Find the number of days in which B can alone complete the work.
   A) 10 days
   B) 12 days
   C) 15 days
   D) 18 days
   E) 21 days
   
   Answer & Explanation

   B) 12 days
   Explanation:
   (A+B+C)’s 1 day’s work = 1/4
   They work for 2 days. So work done after 2 days = 1/4 * 2 = 1/2
   Now B left, so remaining work (1 – 1/2) = 1/2 is to be done by A and C in 3 days.
   1/2 work done in 3 days so complete (1) work done by A and C in 6 days.
   Now (A+B+C)’s 1 day’s work = 1/4 and (A+C)’s 1 day’s work = 1/6
   So B’s 1 day’s work = 1/4 – 1/6 = (3-2)/12 = 1/12
   
   
   
9. The amount that A and B earns is in the ratio 4 : 5. If income of A is increased by 25% and that of B is decreased by 20%, the ratio of their earnings becomes 5 : 4. Find the total of their earnings.
   A) Rs 75,000
   B) Rs 55,000
   C) Rs 50,000
   D) Data inadequate
   E) None of these
   
   Answer & Explanation

   D) Data inadequate
   Explanation:
   Let A’s income = 4x, B’s income = 5x
   After change – A’s income = 125/100 * 4x = 5x and B’s income = 80/100 * 5x = 4x
   So new ratio = 5x : 4x = 5 : 4 which is also given, but it does not give value for x, so data inadequate
   
   
   
10. There is a loss of 25% on an article when it is sold at 2/5 of its Marked Price. How much percent more is Marked Price than Cost Price?
    A) 80.5%
    B) 82%
    C) 87.5%
    D) 89.25%
    E) None of these
    
    Answer & Explanation

    C) 87.5%
    Explanation:
    Let MP = x
    Then SP = 2/5 * x = 2x/5
    Loss is 25%, so CP = [100/(100-25%)] * 2x/5 = 8x/15
    So required % = [(x – 8x/15)/(8x/15)] * 100
    = [(7x/15) / (8x/15)] * 100 = (7/8) * 100 = 87.5%