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  • Question

  • Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?


  • Options
  • A. 3
  • B. 6
  • C. 4
  • D. 2

  • Correct Answer
  • 3 

    Explanation

    Let the number of Rose plants be ?a?.
    Let number of marigold plants be ?b?.
    Let the number of Sunflower plants be ?c?.
    20a+5b+1c=1000; a+b+c=100

     

    Solving the above two equations by eliminating c,
    19a+4b=900

    b = (900-19a)/4 

    b = 225 - 19a/4----------(1)


    b being the number of plants, is a positive integer, and is less than 99, as each of the other two types have at least one plant in the combination i.e .:0 < b < 99--------(2)

    Substituting (1) in (2),

     0 < 225 - 19a/4 < 99

    225 <  -19a/4 < (99 -225)

    => 4 x 225 > 19a > 126 x 4

    => 900/19 > a > 505

     

    a is the integer between 47 and 27 ----------(3)
    From (1), it is clear, a should be multiple of 4.


    Hence possible values of a are (28,32,36,40,44)


    For a=28 and 32, a+b>100
    For all other values of a, we get the desired solution:
    a=36,b=54,c=10
    a=40,b=35,c=25
    a=44,b=16,c=40


    Three solutions are possible.

    • More questions

    • 1. The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

    • Options
    • A. 5 : 7
    • B. 4 : 9
    • C. 1 : 1
    • D. 4 : 7
      • Discuss
    • 2. In a mixture of 35 litres, the ratio of milk and water is 4:1. If 7 litres of water is added to the mixture, the ratio of milk and water of the new mixture will be

    • Options
    • A. 2:1
    • B. 1:2
    • C. 4:5
    • D. 5:4
      • Discuss
    • 3. 
      If the three- fourth of number is subtracted from the number, the value so obtained is 163. What is that number?

    • Options
    • A. 625
    • B. 562
    • C. 632
    • D. 652
      • Discuss
    • 4. 8 litres are drawn from a flask containing milk and then filledwith water. The operation is performed 3 more times. Theratio of the quantity of milk left and total solution is 81/625.How much milk the flask initially holds?

    • Options
    • A. 10 ltr
    • B. 20 ltr
    • C. 30 ltr
    • D. 40 ltr
      • Discuss
    • 5. The square root of 64009 is:

    • Options
    • A. 253
    • B. 347
    • C. 363
    • D. 803
      • Discuss
    • 6. 4, -8, 16, -32, 64, (....)

    • Options
    • A. 128
    • B. -128
    • C. 192
    • D. -192
      • Discuss
    • 7. 
      6.39 x 128.948 + 5.215 ÷ 12.189 + 25.056 =?

    • Options
    • A. 800
    • B. 900
    • C. 850
    • D. 950
      • Discuss
    • 8. 
      A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?

    • Options
    • A. 48
    • B. 60
    • C. 56
    • D. 64
      • Discuss
    • 9. 
      If 1 / 3.718 = .2689, then the value of 1 / .0003718 is?

    • Options
    • A. 2689
    • B. 2.689
    • C. 26890
    • D. .2689
      • Discuss
    • 10. 
      A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the same piece of work is?

    • Options
    • A. 10
    • B. 15
    • C. 12
    • D. 9.6
      • Discuss

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