If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.

Let x be added to each number. The numbers will then be 5 + x, 11 + x, 15 + x and 31 + x. According to question, By cross multiplying, we get : ⇒ (5 \+ x)(31 \+ x) = (15 \+ x)(11 \+ x) ⇒ 155 \+ 5x \+ 31x \+ x 2 = 165 \+ 11x \+ 15x \+ x 2 ⇒ 155 \+ 36x \+ x 2 = 165 \+ 26x \+ x 2 ⇒ 36x \- 26x \+ x 2 \- x 2 = 165 \- 155 ⇒ 10x = 10 ⇒ x = ⇒ x = 1 Hence, 1 is the number that should be added to the given numbers.

Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.

View Answer Bookmark Now

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.

View Answer Bookmark Now

The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages.

View Answer Bookmark Now

Mathematics

If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.

Linear Eqns One Variable

Related Questions

Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.

The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages.