Mixed Quantitative Aptitude Questions Set 13

Word Problems in Quantitative Aptitude Section for SBI PO, NIACL Assistant, IBPS, LIC, RRB, RBI, IPPB and other related exams.

  1. Group A and Group B having some men have average ages 30 and 35 respectively. Both group A and B merge in a single group and their average becomes 33. If the total number of men in groups is 55, find the number of men in group A?
    A) 33
    B) 28
    C) 22
    D) 38
    E) None of these
    View Answer
      Option C
    Solution
    :
    Let number of men in group A and B be x and y respectively>
    So 30x + 35y = 33 (x+y)
    Solving this gives x/y = 2/3
    So number of men in group A = 2/(2+3) * 55 = 22
  2. There are two taps A and B which fill water and milk respectively. Tap A and B can fill the tank in 10 hours and 12 1/2 hours respectively. Tap A is opened in a tank which is already filled with 8% milk. After 2 hours, tap B is also opened and they both fill the tank. Now in what ratio should the mixture from this tank should be mixed with another mixture containing milk and water in the ratio 2 : 3, such that the resultant solution contains half milk and half water?
    A)  2 : 3
    B) 1 : 1
    C) 1 : 2
    D) 2 : 5
    E) None of these
    View Answer
      Option B
    Solution
    :
    Let total capacity of tank = 100 litre
    Given tank is already contain 8% milk
    First Tap A runs for 2 hr. means tank fill by water 2/10=1/5part or 20% water in it
    Now 20 l water and 8 l milk in tank
    Next 72% part of tank still empty
    Both Tap A and B can fill full tank in 1/10 + 1/12.5 = 9/50 means 50/9  hr
    So 72% part fill by tank A and B= 72/100*50/9 = 4hr
    After this water in tank = 4/10 * 100= 40% and milk = 4/12.5 * 100 = 32%
    So Total water in tank = 20+40 = 60l and milk in tank = 40l
    So Water : Milk ratio = 3 : 2
    Given ratio water : milk = 2 : 3
    So by method of allegation:
    3/5——————-2/5
    ———-1/2
    1/10————————1/10
    So Water : Milk ratio = 1 : 1
  3. 8 men can complete a work in 5 days. 12 women can complete in 10 days and 10 children in 24 days. 1 man, 1 woman and 1 child started the work. In how many days will the work get completed if the man did twice the work as woman and also twice the work as child?
    A) 10 days
    B) 9 days
    C) 12 days
    D) 7 days
    E) 13 days
    View Answer
      Option A
    Solution
    :
    Man did twice work from woman and child both. This means woman and child did equal work and Man twice of that. So 2x + x + x = 1, x = 1/4
    Woman did 1/4 of work, child did 1/4 of work and man 2*(1/4) = 1/2 of work
    8 m in 5 days, so 1 man in 40 days, so 1/2 work in 20 days.
    12 w in 10 days, so 1 woman in 120 days, so 1/4 work in 30 days.
    10 c in 24 days, so 1 child in 240 days, so 1/4 work in 60 days.
    So required – 1/20 + 1/30 + 1/60 = 1/10 or 10 days
  4. A rectangular plot has a path in the middle of the plot which is running parallel to the breadth of the plot. The area of rest of the plot leaving the path is 320 m<sup>2</sup>. If the width of the path is 4 m and length of path is greater than its width by 4 m, what is the area of rectangular plot?
    A) 412 m2
    B) 426 m2
    C) 395 m2
    D) 352 m2
    E) None of these
    View Answer
      Option D
    Solution:


    See the figure
    Path of 4 m wide is in the middle parallel to breadth, length of path which is breadth of rectangular plot is 4+4 = 8m
    Path is in the middle, so BC = QS = x m
    Now area of rest of the plot leaving the path is 112 this means area of ABCD + area of PQRS is
    So x*8 + x*8 = 320
    Solve, x = 20
    So length of plot is 20+4+20 = 44, breadth is 8
    So area = 44*8A dishonest shopkeeper
  5. An article is marked at Rs 25,000. It was bought by the trader at successive discounts of 20% and 5%. After this he spent Rs 1,000 on its transportation and finally sold the article for Rs 25,000. What is his profit% in the whole transaction?
    A) 16 2/3%
    B) 28%
    C) 30%
    D) 25%
    E) 20%
    View Answer
      Option D
    Solution:

    Successive discounts of 20% and 5% makes overall discount of  (-20) + (-5) + (-20)(-5)/100 = -25 +1 = -24%
    So he bought the article for [(100-24)/100] * 25000 = 19,000
    Spent 1000 on repairs, so total CP = 1000 + 19000 = 20,000
    SP = 25,000
    So profit% = (5000/20000) * 100
  6. In a business A invested Rs 7000 for 4 months, B invested Rs 8000 for 6 months and C invested Rs 9000 for 5 months. In the last 4 months of the year, they again invested certain amount as Rs 9000, Rs 7000 and Rs 8000 respectively. If at the end of year, a total profit earned is Rs 23,870, then what is the share of B?
    A) Rs 5500
    B) Rs 8280
    C) Rs 8360
    D) Rs 6400
    E) RS 9000
    View Answer
      Option C
    Solution
    :
    Ratio of shares of A : B : C is
    7000*4 + 9000*4 : 8000*6 + 7000*4 : 9000*5 + 8000*4
    7*4 + 9*4 : 8*6 + 7*4 : 9*5 + 8*4
    64 : 76 : 77
    So B got = (76/217) *23,870 = Rs 8360
  7. The ratio of present ages of A and B is in the ratio 7 : x. A is 12 years older than C. After 15 years, C’s age will be 52 years. The sum of the present ages of A and B is 6 less than thrice C’s present age. What is the value of x?
    A) 3
    B) 8
    C) 6
    D) 10
    E) None of these
    View Answer
      Option B
    Solution
    :
    After 15 years, C’s age is 52 years, so present age of C is 37
    A is 12 years older than C, so A’s present age = 37+12 = 49
    Sum of present ages of A and B is 3*C’s-6 so 49+B = 3*37-6, so B = 56
    So A/B = 49/56 = 7/8
    So, x = 8  
  8. A bag contains 3 white, 4 black and 5 green marbles. If 2 marbles are drawn at random from the bag, find the probability that both balls are different in color?
    A) 17/44
    B) 69/220
    C) 47/66
    D) 13/160
    E) 21/170
    View Answer
      Option C
    Solution:
    Case 1: 1 white+1 black
    3C1*4C1/12C2
    Case 2: 1 white+1 green
    3C1*5C1/12C2
    Case 3: 1 green+1 black
    5C1*4C1/12C2
    Add all cases
  9. 40 men can complete a work in 96 days. They all started the work, and after 24, days 20 more men joined. Some men left after further 32 days. If the remaining work now completed in 20 days, what is the number of men who left?
    A) 10
    B) 16
    C) 15
    D) 8
    E) 12
    View Answer
    Option E
    Solution:
    Shortcut:
    40*96 = 40*24 + 60*32 + (60-x)*20
    Solve, x = 12
    OR
    40 men complete work in 96 days. So 60 men in (40*96)/60 = 64 days
    40 men worked for 20 days, after this (40+20) = 60 men worked for 32 days, after this (60-x) men completed the work in 20 more days.
    Let these (60-x) men completes 1 work in y days.
    So (1/96)*24 + (1/64)*32 + (1/y)*20 = 1
    Solve, y = 80
    This means (60-x) men complete 1 work in 80 days
    M1*D1 = M2*D2
    40*96 = (60-x)*80
    Solve, x = 12
  10. There is a loss of 40% on an article when it is sold at 2/5th the previous selling price. What is the actual profit% on it?
    A) 25%
    B) 30%
    C) 33 1/3%
    D) 50%
    E) 22%
    View Answer
      Option D
    Solution:
    Shortcut:

    [(5/2)*(100-40)] – 100 =  150 – 100  = 50%  

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