Question

Three numbers are in the ratio 3:4 : 5. If the sum of the largest and the smallest equals the sum of
the middle number and 52, find the numbers.
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Answer 1

Question :

Three numbers are in the ratio 3:4 : 5. If the sum of the largest and the smallest equals the sum of the middle number and 52, find the numbers.

Answer :

$\sf\pink{Given:}$

• ratio of three numbers is 3:4:5 .

• sum of the largest and the smallest is equal to sum of middle number and 52 , that is :

• let the numbers be 3x , 4x and 5x

$\longrightarrow\sf{ 3x + 5x = 4x + 52}$

$\longrightarrow\sf{ 8x = 4x + 52}$

$\longrightarrow\sf{ 4x = 52}$

$\longrightarrow\sf{ x = \dfrac{52}{4}}$

$\longrightarrow\sf{ x = 13}$

• Smallest number = 3x

$\longrightarrow\sf{ 3\times 13}$

$\longrightarrow\sf{ 39}$

Therefore the smallest number is 39 .

• Middle number = 4x

$\longrightarrow\sf{ 4\times 13}$

$\longrightarrow\sf{ 52}$

Therefore the middle number is 52 .

• Largest number = 5x

$\longrightarrow\sf{ 5\times 13}$

$\longrightarrow\sf{ 65}$

Therefore the largest number is 65 .