Mixed Quantitative Aptitude Questions Set 7

February 13, 2017February 13, 2017 Shubhra

1. How many words can be made out of the letters of the word HEADING such that all vowels occur together?
   A) 120
   B) 144
   C) 124
   D) 136
   E) 720
   
   View Answer

   Option E
   Solution:
   We have H, D, N, G and EAI
   So 5! For these 5 letters (take EAI as single letter because they are to be taken together)
   Now arrangement of EAI is 3!
   So total 5! * 3! = 120 × 6 = 720
   
2. 2 persons same at same time from point A and reach point B at 6 PM and 9 PM respectively. The average speed of one is 25 km/hr and that of another is 15 km/hr respectively. What should be there average speed (approximate) such that both reach at 8 PM?
   A) 15 km/hr
   B) 20 km/hr
   C) 17 km/hr
   D) 16 km/hr
   E) 18 km/hr
   
   View Answer

   Option C
   Solution:
   Let distance from A to B is ‘d’ and time taken to reach at 8 PM is ‘t’
   Then with 6 PM, time becomes ‘t-2’, so d/(t-2) = 25
   With 9 PM, time becomes ‘t+1’, so d/(t+1) = 15
   Solve the equations, t = 6.5 hrs, d = 112.5 km
   So speed to reach at 1 PM = 112.5/6.5 = 17 km/hr
   
3. Rekha’s age is 4 years less than that of Sheetal who age is 8 years less than Ravina. If seven years hence, the ratio of ages of Ravina to Rekha will be 13 : 7, then find the present age of Sheetal.
   A) 11 years
   B) 10 years
   C) 15 years
   D) 18 years
   E) 13 years
   
   View Answer

   Option A
   Solution:
   Sheetal = A, Rekha = B, Ravina = C
   A = B+4
   A = C-8
   B+7 / C+ 7 = 7/13
   Or (A-4)+7 / (A+8)+7 = 7/13
   A+3 / A+15 = 7/13
   A = 11 = Sheetal’s present age
   
4. A bag contains 7 red balls and 5 white balls. 2 balls are drawn at random. What is the probability that both balls are red in color?
   A) 2/33
   B) 7/44
   C) 8/33
   D) 7/22
   E) None of these
   
   View Answer

   Option D
   Solution:
   Total balls = 7+5 = 12
   So required prob. = ⁷C₂ / ¹²C₂ = 7/22
   
5. The incomes of 2 persons A and B is in the ratio 2 : 3. Their expenditures are in the ratio 1 : 2 respectively. If both save Rs 13,000, then what is B’s income?
   A) Rs 39000
   B) Rs 26000
   C) Rs 29000
   D) Rs 32000
   E) Rs 48000
   
   View Answer

   Option A
   Solution:
   Incomes 2x and 3x
   Expenditures y and 2y
   So 2x – y = 13000
   And 3x – 2y = 13000
   Solve both equations, x = 13,000
   So B’s income = 3*13000 = Rs 39000
   
6. A man buys 30 articles at the marked price of 24 articles. If he sells the articles by giving 2% discount, what will be the overall profit% made?
   A) 25.5%
   B) 22.5%
   C) 20.5%
   D) 18.5%
   E) 23.5%
   
   View Answer

   Option B
   Solution:
   Let MP of 1 article = Re 1
   CP of 30 articles = MP of 24 articles = Rs 24
   MP of 30 articles = Rs 30
   So after discount of 2%, SP of 30 articles = 98/100 * 30 = Rs 29.4
   So profit% = (29.4 – 24)/24 * 100 = 22.5%
   
7. 25 men can complete a work in 40 days. They start the work, but because of some reason only one-third work could be completed after 24 days. How many extra men should join them in order to complete the work in 36 days?
   A) 75
   B) 82
   C) 87
   D) 58
   E) 65
   
   View Answer

   Option A
   Solution:
   After 24 days, the work is to be completed in (36-24) = 12 days
   Remaining work = 1 – 1/3 = 2/3
   Let x extra men are needed. So,
   25 * 24 * 2/3 = (x+25) * 12 * 1/3
   Solve, x = 75
8. If an item is sold at 3/5th of its actual selling price, the profit made is 20%. Now if the same item is sold at 25% less than the actual selling price, what will be the profit%/loss%?
   A) 48%
   B) 52%
   C) 45%
   D) 53%
   E) 50%
   
   View Answer

   Option E
   Solution:
   Profit is 20%. So,
   (3/5 SP – CP)/CP * 100 = 20
   This gives SP = 2*CP
   Now product sold at 25% less S.P. i.e. 75/100 or 3/4 of S.P.
   Profit/loss% = (3/4 SP – CP)/CP * 100
   Put SP = 2CP
   Solve, Profit% is 50% (+50 means profit)
   
9. A solution contains ingredients P, Q, and R in the ratio 2 : 3 : 1 and another solution contains them in the ratio 1 : 3 : 4 respectively. If both solutions are mixed in the ratio 5 : 6. What is the percentage (approximate) of C in the final solution?
   A) 10%
   B) 40%
   C) 20%
   D) 35%
   E) 25%
   
   View Answer

   Option D
   Solution:
   Ratio of C to A+B in 1st solution = 1 : (2+3) = 1 : 5
   Ratio of C to A+B in 2nd solution = 4 : (1+3) = 4 : 4 = 1 : 1
   They are mixed in ratio 5 : 6
   So ratio of C to (A+B) in final solution = 1/6 * 5 + 1/2 * 6 : 5/6 * 5 + 1/2 * 6 = 23 : 43
   So, percentage of C = 23/(23+43) * 100 = 35%
   
10. The total population of a town is 1,20,000. It has 70% males and rest females. If 85% of males and 50% of females are literate, then what is the total number of illiterates in the town?
    A) 32800
    B) 12600
    C) 23400
    D) 30600
    E) 20100
    
    View Answer

    Option D
    Solution:
    Males = (70/100)*1,20,000 = 84,000 so females = 1,20,000 – 84,000 = 36,000
    Male illiterates = (15/100)*84,000 = 12,600
    Female illiterates = (50/100)* 36,000 = 18,000
    Total 12600 + 18000
    

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