Question

Differeence between two number is 30. Twice
the greater number is less than 7 times the
smallere number by 5
find the numbers.​

Answer 1

Given :-

▪ Difference between two numbers is 30.

▪ Twice the greater number is less than 7 times the smaller number by 5.

To Find :-

▪ Numbers.

Solution :-

Let the numbers be x and y, respectively.

Also, Let the greater number be x and the smaller one be y.

According to the question,

Case 1 :

☞ Difference between two numbers is 30.

⇒ x - y = 30

⇒ x = y + 30 ...(1)

Case 2 :

☞ Twice the greater number i.e., x is less than 7 times the smaller number i.e., y by 5.

⇒ 2x + 5 = 7y

⇒ 2(y + 30) + 5 = 7y [ from (1) ]

⇒ 2y + 60 + 5 = 7y

⇒ 5y = 65

⇒ y = 13

Substituting the value of y in (1), we get

⇒ x = y + 30

⇒ x = 13 + 30

⇒ x = 43

Hence, The numbers are 43 and 13.

Answer 2

Solution :-

Let's assume that, two numbers be "R" and "S".

According to first statement,

☞ Difference between two number is 30.

↪ R - S = 30

↪R = S + 30 --------(1)

According to second statement,

☞ Twice the greater number is less than 7 times the smaller number by 5.

↪2R + 5 = 7S ----------(2)

[ Put Eqn. (1) value in Eqn. (2) : We get, ]

↪2(S + 30) + 5 = 7S

↪2S + 60 + 5 = 7S

↪2S + 65 = 7S

↪2S - 7S = -65

↪-5S = 65

↪${\red{\bold{S = 13}}}$

[ Put S = 13 in eqn. (1) ]

↪ R = S + 30

↪ R = 13 + 30

↪ ${\blue{\bold{R = 43}}}$

Hence,

• The numbers are 43 and 13.