Quantitative Aptitude: Data Interpretation Questions Set 40

Data Interpretation Questions (DI) for IBPS PO 2017, IBPS PO, NIACL, NICL, SBI PO RBI Grade B, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams. Casellete based Data Interpretation Set IBPS PO 2017

Direction (1-5): Study the following information and answer the questions that follow:

Vishal and Shekhar have some toffees initially. Everyday Vishal and Shekhar buy a fixed number of toffees. The number of toffees that they buy each day is different from other’s number. After 4 days, they have equal number of toffees. After 12 days Vishal has 8 (16/23)% more toffees than Shekhar. After 13 days, Sunidhi who has no toffee initially, took 6 toffees from Vishal and 3 toffees from Shekhar, as a result now Vishal has 6 toffees more than Shekhar. After 15 days, they all clubbed together their toffees and divided equally among the three. Now each of them has 71 toffees. Based on this information answer the questions that follows.

  1. How many toffees Vishal had initially?
    A) 50
    B) 48
    C) 56
    D) 52
    E) 64
    View Answer
    Option D
    Solution
    :
    Let Vishal has V toffees initially and he buys A toffees each day
    Let Shekhar has S toffees initially and he buys B toffees each day
    After 4 days, they have equal number of toffees.
    hence V+4A = S+4B
    => V-S=4(B-A) —- (i) After 12 days Vishal has 8 (16/23)% =200/13% more toffees than Shekhar
    V + 12A = (S+ 12 B)* (1+2/23)
    => V+12A =25/23 * (S+12B) —– (ii) After 13 days, Sunidhi who has no toffee initially, took 6 toffees from Vishal and 3 toffees from Shekhar, as a result now Vishal has 6 toffees more than Shekhar.
    Toffees with Vishal after 13 days = V+13B ; when 6 toffees given to Sunidhi now he has V+13A-6
    Toffees with Shekhar after 13 days = S +13B; when 3 toffees given to Sunidhi now he has S+13B -3
    also ;
    V+13A-6 = (S+13B -3) + 6
    =>V+13A = S+13B+9
    =>V-S=13(B-A)+9 ———– (iii)
    After 15 days, they all clubbed together their toffees and divided equally among the three. Now each of them has 71 toffees.
    All the toffees that they have after 15 days is due to Vishal and Shekhar, as Sundihi had 0 toffees initially
    So V+15A + S+15B=3*71=213 —- (iv)
    Equate eq (i) and (iii) for V-S = V-S in each equation , so we have now
    4(B-A)= 13(B-A)+9
    We get A-B= 1
    A=1+B—-(v)
    put this in eq (i)
    S-V=4
    S=V+4— (vi)
    Put A=1+B and S=V+4
    in eq (ii) and (iv) to get two equations with two variable
    we will get
    V+12B=88
    and
    V+15B=97
    solve and get
    B=3 and V=52
    hence
    A=4 and S=56
    so now we have all the required value; keep them handy
    V=52; A=4
    S=56; B=3
    So Vishal has 52 toffees initially
  2. How many toffees Shekhar buys everyday?
    A) 2
    B) 3
    C) 4
    D) 5
    E) 6
    View Answer
    Option B
  3. After 14 days how many toffees did Shekhar and Sunidhi had in total?
    A) 101
    B) 104
    C) 107
    D) 110
    E) 113
    View Answer
    Option B
    Solution
    :
    After 14 days Shekhar had 56+14*3 -3 =95 toffees (as 3 toffees have been taken by Sunidhi)
    Sunidhi has 9 toffees
    total=95+9=104
  4. By what percent the number of toffees that Shekhar had was less than that of Vishal after 11 days?
    A) 7.90%
    B) 8.24%
    C) 9.27%
    D) 6.24%
    E) 7.29%
    View Answer
    Option E
    Solution
    :
    After 11 days
    Vishal=52+11*4=96
    Shekhar=56+11*3=89
    Required % = (96-89)/96 *100 =
  5. If Vishal and Shekhar keeps on buying toffees in same manner, then the number of toffees they will have in total after 50 days is?
    A) 402
    B) 503
    C) 387
    D) 457
    E) 458
    View Answer
    Option C
    Solution
    :
    After 15 days they had 71 toffees each
    So After 50 days
    71+71+(50-15)*4 + (50-15)*3= 387

Direction (6-10): Study the following information and answer the questions that follow:

In a bilateral cricket series between India and Australia, the probability that India wins the first game is 0.4. If India wins any game, the probability that it wins the next game is 0.3; otherwise the probability is 0.2.

  1. Find the probability that India wins the first two games.
    A) 0.08
    B) 0.32
    C) 0.18
    D) 0.12
    E) None of these
    View Answer
    Option D
    Solution
    :
    P(Win first game)* P(Win second game)= 0.4*0.3=0.12
  2. Find the probability that India wins at least one of the first two games.
    A) 0.48
    B) 0.32
    C) 0.56
    D) 0.52
    E) 0.58
    View Answer
    Option D
    Solution
    :
    P(won at least 1 game)= 1- P(won no games)
    =1- [P(lost 1st game)*P(lost second game)] =1- [(1-0.4)*(1-0.2)] (0.2) in the second bracket because after losing the first game the probability of wining the second match is 0.2. So 1-0.2 is the probability of losing that game too.
  3. Find the probability that India wins the first three games.
    A) 0.028
    B) 0.030
    C) 0.032
    D) 0.036
    E) 0.044
    View Answer
    Option D
    Solution
    :
    0.4*0.3*0.3= 0.036
  4. Find the probability that India wins exactly one of the first three matches.
    A) 0.416
    B) 0.396
    C) 0.096
    D) 0.404
    E) 0.214
    View Answer
    Option D
    Solution
    :
    This problem can be solved in three parts
    Part 1- India wins first game and loses second and third
    part 2= Lose + Win + Lose
    Part 3= Lose + Lose+ Win
    P (Part 1)= India wins first game * India loses second game* India loses third game
    = 0.4 * (1-0.3)* (1-0.2)= 0.4*0.7*0.8 = 0.224
    P (Part2)= India loses first game * Wins second game * Loses third game
    = (1-0.4)* 0.2 * (1-0.3)= 0.6*0.2*0.7= 0.084
    P (Part 3)= L*L*W = (1-0.4)* (1-0.2) * 0.2= 0.6*0.8*0.2= 0.096
    P= P1+P2+P3= 0.404
  5. Find the probability that India wins exactly one of the first two games.
    A) 0.20
    B) 0.40
    C) 0.44
    D) 0.36
    E) 0.28
    View Answer
    Option B
    Solution
    :
    Part 1= Won first * Lost Second= 0.4* (1-0.3)= 0.4*0.7=0.28
    Part 2= Lost First* Won second = (1-0.4)*0.2= 0.6*0.2=0.12
    P= 0.28+0.12=0.40

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