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

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​A = 3 × 10 = 30 years

​B = 5 × 10 = 50 years

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∴ Difference = 50 - 30 = 20 years

Question: In a mixture of milk and water, the ratio is 7 : 5. If 6 liters of water is added, the new ratio becomes 7 : 6. What was the original amount of milk in the mixture?

Solution:

ধরি, শুরুতে দুধ ছিল = 7x লিটার,

পানি ছিল = 5x লিটার।

এখন 6 লিটার পানি যোগ করলে,

নতুন পানি = 5x + 6 লিটার

ATQ,

7x/(5x + 6) = 7/6

⇒ 6 × 7x = 7 × (5x + 6)

⇒ 42x = 35x + 42

⇒ 7x = 42

⇒ x = 6

∴ দুধের পরিমাণ = 7x = 7 × 6 = 42 লিটার

Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?

Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles

∴ Required number of motorcycles = 40 - 24 = 16

So the ferry can carry 16 more motorcycles along with the 15 trucks.