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Mathematics

42 mangoes are to be distributed among some boys and girls. If each boy is given 3 mangoes, then each girl gets 6 mangoes; and if each boy gets 5 mangoes, then each girl gets 3 mangoes. The number of boys and girls will be :

  1. boys = 4, girls = 6

  2. boys = 6, girls = 4

  3. boys = 7, girls = 3

  4. boys = 3, girls = 7

Linear Equations

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Answer

Let x be the number of boys and y be the number of girls,

Given,

Case 1:

If each boy is given 3 mangoes, then each girl gets 6 mangoes.

⇒ 3x + 6y = 42     …….(1)

Case 2:

If each boy is given 5 mangoes, then each girl gets 3 mangoes.

⇒ 5x + 3y = 42     ….(2)

Multiply equation by 2 we get,

⇒ 2(5x + 3y = 42)

⇒ 10x + 6y = 84     ……(3)

Subtracting equation (1) from (3), we get:

⇒ 10x + 6y - (3x + 6y) = 84 - 42

⇒ 10x + 6y - 3x - 6y = 84 - 42

⇒ 7x = 42

⇒ x = 427\dfrac{42}{7} = 6.

Substituting value of x in equation 1, we get :

⇒ 3x + 6y = 42

⇒ 3(6) + 6y = 42

⇒ 18 + 6y = 42

⇒ 6y = 42 - 18

⇒ 6y = 24

⇒ y = 246\dfrac{24}{6} = 4.

Thus, no. of boys = 6, no. of girls = 4.

Hence, option 2 is the correct option.

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