Question: The present ages of A and B are in the ratio 3 : 5. After 10 years, the ratio of their ages will be 4 : 6. What is the difference in their present ages?

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​Solution:

​Let the present ages be,

​A = 3x and B = 5x

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​Ages after 10 years,

​A = 3x + 10

​B = 5x + 10

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​According to the problem, the ratio becomes 4 : 6

​(3x + 10) : (5x + 10) = 4 : 6

⇒ ​​(3x + 10)/(5x + 10) = 4/6

​⇒ ​​3(3x + 10) =2(5x + 10)

​⇒ ​​9x + 30 = 10x + 20

⇒ ​​​10x - 9x = 30 - 20

∴ ​x = 10

​

​A = 3 × 10 = 30 years

​B = 5 × 10 = 50 years

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∴ Difference = 50 - 30 = 20 years

Question: When 25% of the first number is added to the second number, the second number becomes 3/2 times the first number. What is the ratio of the first number to the second number?

Solution:

Let the first number = x

and the second number = y.

According to the question,

y + 25% of x = (3/2)x

⇒ y + (25/100)x = (3/2)x

⇒ y + (1/4)x = (3/2)x

⇒ y = (3/2)x - (1/4)x

⇒ y = (6 - 1)x/4

⇒ y = 5x/4

∴ y = 5x/4

Therefore, x : y = 4 : 5 

ধরি: তিন কোণ = $2x, 5x, 8x$
$2x + 5x + 8x = 180$
$15x = 180$ ⇒ $x = 12$
বৃহত্তম কোণ = $8 \times 12 = 96^\circ$