Question

Maths1 assistant
1) A two digit number is 4 times the sum of its digits. If we interchange the digits, the number obtained is 9 less than 2 times the original number. Then find the number.
2)The ratio of number of mango trees to chikoo trees in an orchard is 2:3.If 5 more trees of each type are planted the ratio of trees would be 5:7.Then find the number of mango and chikoo trees in the orchard.​

Answer 1

Answer:

36

20 and 30

Step-by-step explanation:

Let the unit digit be 'y' and the tens digit be 'x'.Thus, the number be 10x + y.

⇒ number = 4 times sum of x and y

⇒ 10x + y = 4(x + y)

⇒ 6x = 3y      ⇒ 2x = y

If we interchange the digits, the number obtained is 9 less than 2 times the original number. . And the new number becomes 10y + x.

⇒ 10y + x = 2(10x + y) - 9

⇒ 9 = 19x - 8y

⇒ 9 = 19x - 8(2x)            [y = 2x]

⇒ 9 = 3x          ⇒ 3 = x

     Thus, y = 2x = 2(3) = 6

∴ Required number is xy = 36

Let the number of mango trees and chikoo trees be 2x and 3x respectively.  When 5 more trees are planted, mango trees are 2x + 5 and chikoo trees are 3x + 5.   Given, their ratio is 5 : 7.

⇒ (2x + 5)/(3x + 5) = 5/7

⇒ 7(2x + 5) = 5(3x + 5)

⇒ 14x + 35 = 15x + 25

⇒ 10 = x

  Hence,

Mango tress = 2x = 2(10) = 20

Chikoo trees = 3x = 3(10) = 30