Math, asked by ProPlayer00, 1 month ago

The ages of Anil & Sohan are in the ratio 3:8 four years from the ration of their ages
will be 1:2. Find their present age

Answers

Answered by VidishaRaj

$Correct Question :-The ages of Anil & Sohan are in the ratio 3:8. Four years from now the ratio of their ages will be 1:2. Find their present ages. Required Answer :-Present age of Anil is 6 years.Present age of Sohan is 16 years.Explanation :-Given :-Ratio of ages of Anil & Sohan = 3:8Four years from now ratio of their ages will be = 1:2To Find :-Their present ages?Solution :-Let their present ages be 3n years & 8n years.So, four years from now their ages will be (3n + 4) years & (8n + 4) years.According to the question,Four years from now ratio of their ages will be 1:2.Therefore,⇒ \sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}8n+43n+4=21By cross multiplication,⇒ \sf 2(3n + 4) = 1(8n + 4)2(3n+4)=1(8n+4)⇒ \sf 6n + 8 = 8n + 46n+8=8n+4⇒ \sf 8n - 6n = 8 - 48n−6n=8−4⇒ \sf 2n = 42n=4⇒ \sf n = {\cancel{\dfrac{4}{2}}}n=24➠ \bf\red{n = 2}n=2Hence,↦ Present age of Anil = 3n↦ Present age of Anil = 3 × 2➦ Present age of Anil = 6 yearsAlso,↦ Present age of Sohan = 8n↦ Present age of Sohan = 8 × 2➦ Present age of Sohan = 16 years∴ Hence, present ages of Anil & Sohan are \boxed{\bf{6\: years}}6years & \boxed{\bf{16\: years}}16years .Let's Verify :-We know that,↪ \sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}8n+43n+4=21Put of n = 2 we get,↪ \sf \dfrac{(3\:\times\:2) + 4}{(8\:\times\:2) + 4} = \dfrac{1}{2}(8×2)+4(3×2)+4=21↪ \sf \dfrac{6 + 4}{16 + 4} = \dfrac{1}{2}16+46+4=21↪ \sf {\cancel{\dfrac{10}{20}}} = \dfrac{1}{2}2010=21↪ \sf \dfrac{1}{2} = \dfrac{1}{2}21=21➢ \bf \purple{LHS = RHS}LHS=RHSHence, Verified ✔▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬$

Answered by DearBrainly

Answer:

Appropriate Question :-

The ages of Anil & Sohan are in the ratio 3:8. Four years from now the ratio of their ages will be 1:2. Find their present ages.

Required Answer :-

Present age of Anil is 6 years.

Present age of Sohan is 16 years.

Explanation :-

Given :-

Ratio of ages of Anil & Sohan = 3:8

Four years from now ratio of their ages will be = 1:2

To Find :-

Their present ages?

Solution :-

Let their present ages be 3n years & 8n years.

So, four years from now their ages will be (3n + 4) years & (8n + 4) years.

According to the question,

Four years from now ratio of their ages will be 1:2.

Therefore,

⇒ $\sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}$

By cross multiplication,

⇒ $\sf 2(3n + 4) = 1(8n + 4)$

⇒ $\sf 6n + 8 = 8n + 4$

⇒ $\sf 8n - 6n = 8 - 4$

⇒ $\sf 2n = 4$

⇒ $\sf n = {\cancel{\dfrac{4}{2}}}$

➠ $\bf\red{n = 2}$

Hence,

↦ Present age of Anil = 3n

↦ Present age of Anil = 3 × 2

➦ Present age of Anil = 6 years

Also,

↦ Present age of Sohan = 8n

↦ Present age of Sohan = 8 × 2

➦ Present age of Sohan = 16 years

∴ Hence, present ages of Anil & Sohan are $\boxed{\bf{6\: years}}$ & $\boxed{\bf{16\: years}}$ .

Let's Verify :-

We know that,

↪ $\sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}$

Put of n = 2 we get,

↪ $\sf \dfrac{(3\:\times\:2) + 4}{(8\:\times\:2) + 4} = \dfrac{1}{2}$

↪ $\sf \dfrac{6 + 4}{16 + 4} = \dfrac{1}{2}$

↪ $\sf {\cancel{\dfrac{10}{20}}} = \dfrac{1}{2}$

↪ $\sf \dfrac{1}{2} = \dfrac{1}{2}$

➢ $\bf \purple{LHS = RHS}$

Hence, Verified ✔

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