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Quantitative Aptitude (QA) Test - 36
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Quantitative Aptitude (QA) Test - 36
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  • Question 1/10
    3 / -1

    Satendra and Punit travel from places S and P, respectively towards each other, Satendra started his journey 2 hours earlier than Kamal. The speed of Satendra and Punit are 45 km/h and 54 km/h respectively and distance between place S and place P is 882 km. After the meeting, how much distance travelled by Satendra to reach place P?

    Solutions

    Distance covered by Satendra in 3 hours = 2 * 45 = 90 km

    Remaining distance = 882 - 90 = 792 km

    Meeting time = 792/(45 + 54) = 8 hours

    So, after meeting, distance covered by Satendra = 8 * 54 = 432 km

     

  • Question 2/10
    3 / -1

    At what time after 5 : 10 am, the acute angle made by the minute and hour-hand is decreased by 40% that of at 5 : 10 am, for the first time?

    Solutions

    At 5:00, hour hand must be at 5 * 30 = 150 degree from 12 (clockwise).

    Minute hand of the clock moves with 6 degree per minute speed and hour hand moves at 1/2 degree per minute.

    Angle between two hands at 5 : 10 am = 5 * 30 + 10 * 1/2 - 10 * 6 = 95°

    Now, angle decreased by 40% = 95 * 60/100 = 57°

    Let now minutes hand at x min.

    So, 5 * 30 + x * 1/2 - x * 6 = 57°

    => 11x/2 = 150 - 57 = 93

    => x = 186/11 min

    So, at 5h 186/11 min the required angle will be formed.

     

  • Question 3/10
    3 / -1

    A seller sells bedsheets, pillows, and curtains. At the end of the year, he earned 40% profit on pillows and 25% profit on bedsheets. Pillows contributed 35% of the total sales in rupees and the total sales in rupees from bedsheets is 50% more than that of pillows. If he has earned 20% profit overall, how much profit or loss made on curtains?

    Solutions

    Let the total cost price of all articles be Rs. 100k and total selling price of all articles be Rs. 120k.

    Selling price of pillows = 35% of Total selling price = 0.35 (120k) = Rs. 42k

    Selling price of bedsheets = 150% of selling price of pillows = 3/2 * 42k = Rs. 63k

    So, selling price of curtains = 120k - 42k - 63k = Rs. 15k

    he earned 40% profit on pillows and 25% profit on bedsheets.

    Cost price of pillows = 100/140 * 42k = Rs. 30k

    Cost price of bedsheets = 100/125 * 63k = Rs. 50.4k

    So, cost price of curtains = 100k - 30k - 50.4k = Rs. 19.6k

    Loss percentage on curtains = (19.6k - 15k)/19.6k * 100 = 23.4%

     

  • Question 4/10
    3 / -1

    Two containers X and Y contained pure coconut oil and neither container was filled completely. 80% of the coconut oil from container X was transferred to container Y. Now, 60% of the coconut oil of container Y was then transferred ack to container X which resulted in the ratio of the quantities of coconut oil in containers X and Y is 23: 12. What was the ratio of the initial quantity of coconut oil in containers X and Y?

    Solutions

    Let the initial quantities of coconut oil in containers X and Y be x and y respectively.

    After the first operation, container X would have 0.2x and container Y would have (0.8x + y).

    After the second operation, container X would have [0.2x + 0.6(0.8x + y)] and container Y would have [0.4(0.8x + y)].

    According to the question,

    => 12(x + 3(0.8x + y) = 23 * 2(0.8x + y)

    => 6(x + 2.4x + 3y) = 18.4x + 23y

    => 20.4x + 18y = 18.4x + 23y

    => 2x = 5y

    => x/y = 5/2

    Hence, ratio of the initial quantity of coconut oil in containers X and Y = 5: 2

     

  • Question 5/10
    3 / -1

    There are three departments IT, HR, and Admin in the company. The average salary of the employees of all the three departments put together is Rs. P. The average per employee salary of IT and HR put together is Rs. 7100. The average per employee salary of HR and Admin put together is Rs. 7600. The average per employee salary of IT and Admin put together is Rs. 7900. Find the range of P.

    Solutions

    Let number of employees in IT, HR, and Admin departments are m, n, and p, respectively and total salary of employees in IT, HR, and Admin departments are X, Y, and Z, respectively.

    According to the question,

    X + Y = 7100(m + n) ---(1)

    Y + Z = 7600(n + p) ---(2)

    Z + X = 7900(m + p) ---(3)

    Adding equations (1), (2), and (3), we get

    2(X + Y + Z) = 15000m + 14700n + 15500p

    => X + Y + Z = 7500m + 7350n + 7750p

     

  • Question 6/10
    3 / -1

    If √(7x + 12) + √(7x - 12) = 2(4 + √10), then what is the value of √(14x + 21)?

    Solutions

    √(7x + 12) + √(7x - 12) = 2(4 + √10)

    => √(7x + 12) + √(7x - 12) = 8 + 2√10

    => √(7x + 12) + √(7x - 12) = √64 + √40

    So, √(7x + 12) = √64 and √(7x - 12) = √40

    => 7x + 12 = 64

    => x = 52/ 7

    Thus, √(14x + 21) = √(14 * 52/7 + 21) = √125 = 5√5

     

  • Question 7/10
    3 / -1

    In a company there are three types of cake baking machines A, B, and C which bake 25% , 35%, and 40% of the total cakes respectively on a particular day. On the next day, 2%, 4% and 5% of cakes baked by A, B, and C are rotten, respectively. What is the percentage of good cakes on the next day?

    Solutions

    Let on a particular day, they make 100 cakes. So, machine A bakes 25 cakes, machine B bakes 35 cakes and machine C bakes 40 cakes respectively.

    Percentage of good cakes on the next day = (25 * 0.98 + 35 * 0.96 + 40 * 0.95)/100 * 100 = 96.1%

     

  • Question 8/10
    3 / -1

    The amount of work that A, B, and C can alone do in a day, are in harmonic progression. Ratio of efficiency of A and C is 5: 2. If A, B, and C together started the work and A left 2 days before the completion of work and B left 4 days before the completion of the work, then whole work gets completed in 18 days. In how much time A and B together can complete the whole work?

    Solutions

    Let amount of work done by A, B, and C alone in a day are a units, b units, and c units, respectively.

    Ratio of efficiency of A and C is 5: 2.

    Let a = 5k units, and C = 2k units

    Now, a, b, and c are in H.P.

    So, 2/b = 1/a + 1/c

    => 2/b = 1/5k + 1/2k

    => b = 20k/7

    A worked for 16 days, B worked for 14 days and C worked for 18 days.

    So, total unit of work = 16 * 5k + 14 * 20k/7 + 18 * 2k = 156k units

    Total work done by A and B in = 156k/(5k + 20k/7) = 19(47/55) days

     

  • Question 9/10
    3 / -1

    Ramlal deposits a sum of Rs. M in a bank at a certain rate of interest compound interest. The amount becomes Rs. 27M after three years by compounding annually. Instead, if the bank had compounded half yearly, what is the additional amount Ramlal would have received in terms of M?

    Solutions

    Sum = Rs. M; In 3 years, amount = Rs. 27M

    Let rate of interest = k%;

    So, M(1 + k/100)3 = 27M

    => (1 + k/100)3 = 27

    => 1 + k/100 = 3

    => k = 200%

    Now, compounding half yearly, the amount will be = M(1 + 100/100)6 = M * 26 = Rs. 64M

    Hence, additional amount received = 64M - 27M = Rs. 37M

     

  • Question 10/10
    3 / -1

    Madhav set up a fast-food stall and gets a starting profit of Rs. 5000 per month. During the first year of his sales, he receives a monthly increment in his profit of Rs. 200 starting from the second month. During the second year, he receives a monthly increment in his profit of Rs. 400, a monthly increment in his profit of Rs. 600 for the third year and so on. Find the total profit received by Madhav at the end of 4 years. (Assume that the profit he receives during the last month of a year is same as that during the first month of the next year).

    Solutions

    The profit of Madhav during the last month of the 1st year = 5000 + (12 − 1) 200 = Rs. 7200

    The profit of Madhav during the last month of the second year = Rs. [7200 + 11(400)] = Rs. 11600

    The profit of Madhav during the last month of the third year = 11600 + 11 (600) = Rs. 18200

    Hence, total salary the person has earned in four years:

     

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