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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


  • 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.


  • Permutation and Combination problems


    Search Results


    • 1. There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card ?

    • Options
    • A. 4 x 3^4
    • B. 3^4
    • C. 4^3
    • D. 3 x 4^3
    • Discuss
    • 2. A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

    • Options
    • A. 340
    • B. 210
    • C. 290
    • D. 252
    • Discuss
    • 3. A standard deck of playing cards has 13 spades. How many ways can these 13 spades be arranged?

    • Options
    • A. 13!
    • B. 13^2
    • C. 13^13
    • D. 2!
    • Discuss
    • 4. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

    • Options
    • A. 48
    • B. 64
    • C. 63
    • D. 45
    • Discuss
    • 5. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

    • Options
    • A. 564
    • B. 735
    • C. 756
    • D. 657
    • Discuss
    • 6. In how many ways can 100 soldiers be divided into 4 squads of 10, 20, 30, 40 respectively?

    • Options
    • A. 1700
    • B. 18!
    • C. 190
    • D. None of these
    • Discuss
    • 7. What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?

    • Options
    • A. 28450
    • B. 26340
    • C. 32640
    • D. 36450
    • Discuss
    • 8. There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical ?

    • Options
    • A. 23
    • B. 432
    • C. 22
    • D. 431
    • Discuss
    • 9. Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without repetition. Number may be of any of the form like 2,24,684,4862 ?

    • Options
    • A. 133345
    • B. 147320
    • C. 13320
    • D. 145874
    • Discuss
    • 10. A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ? A) 24 - 1 B) 2425-1 C) (24-1)(23-1)25 D) None

    • Options
    • A. A
    • B. B
    • C. C
    • D. D
    • Discuss


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