Question

this question is only for matharybathta​

Answer 1

Given :-

• Money gave to wife = 50% of his saving of Rs.84100.
• Son A present age = 15 Years.
• son B present age = 13 Years.
• Rate of interest = 5 % compounded Annually.
• At the age of 18 They got same Amount .

To Find :-

• Share of B ?

Formula used :-

• Amount (when Rate is compounded Annually) = P* [ 1 + (R/100) ]^T

Solution :-

It is given that, Present age of A & B are 15 & 13 respectively, and Amount will be same when both turned 18.

So,

→ A will be of age 18 after = 18 - 15 = 3 Years.

→ B will be of age 18 after = 18 - 13 = 5 Years.

So, we can conclude That,

→ Time for which A received interest = 3 Years.

→ Time for which B received interest = 5 Years .

________________

Now,

it is given That , the man gave 50% of his saving of 84,100 to his wife.

So, we can say That, Rest one Left is also 50% and that is Equal to Half Rs.84,100 = Rs.42050

Hence,

→ Total Amount Distributed Among Both Son = Rs.42,050

_________________

Now, Let us Assume That, share of B is Rs.x .

Than,

→ share of A = Rs.(42050 - x)

_________________

Now, we have , share of Both, Time of Both, and Rate of both is 5% and Amount will be Equal.

Comparing Both Amount Now :-

⟿ A amount after 3 Years = B amount after 5 Years.

⟿ (42050 - x)[ 1 + (5/100)]³ = x[ 1 + (5/100)]^5

⟿ (42050 - x) / x = [ 1 + (5/100)]^5 / [ 1 + (5/100)]³

Now, using (a^m)/(a^n) = a^(m - n) in RHS we get,

⟿ (42050 - x) / x = [ 1 + (5/100)]²

⟿ (42050 - x) / x = [ 1 + (1/20)]²

⟿ (42050 - x) / x = (21/20)²

⟿ (42050 - x) / x = 441/400

Cross - Multiply Now,

⟿ 400(42050 - x) = 441x

⟿ 400*42050 - 400x = 441x

⟿ 400*42050 = 441x + 400x

⟿ 841x = 400 * 42050

Dividing Both sides by 841 Now,

⟿ x = 400 * 50

⟿ x = Rs.20000 (Ans.)

Hence, Share of B was Rs.20000.

_____________________

Answer 2

Given :-

• Saving of a person = Rs 84100

• He gave 50% to his wife.

• And remaining 50% divided between his two sons .

• Age of A = 15 years

• Age of B = 13 years

• Sum is divided in such a way that the compound interest on the sum will result in equal to both sons money .

• Rate of interest = 5% . Interest is applied till 18 year age of both .

____________________

→ Now The person give 50% to his wife which amounts = $\frac{84100 \times 50}{100}$

→ Amount given to wife = Rs 42050 .

So remaining sum is also Rs 42050 .

He divided Rs 42050 among his two sons.

✧ Let's assume that he gave X rupees to A and Rs 42050-x to B .

$\boxed{Compound\: interest \:= P\times{1 + \frac{R}{100}}^{n}}$

Let's take A firstly .

→ $(X)\times{1 + \frac{5}{100}}^{3}$

→ $X \times{ \frac{105}{100}}^{3}$

→ $X \times { \frac{21}{20}}^{3}$

↑ This is the amount given to A .

Let's take B now .

→ $(42050 - X)\times{1 + \frac{5}{100}}^{5}$

→ $(42050- X) \times{ \frac{105}{100}}^{5}$

→ $(42050-X) \times { \frac{21}{20}}^{5}$

↑ This is the amount given to B.

Putting equalent both sons amount

→ X (21/20)³ = (42050 - X)×(21/20)^5

→ x = (42050 -x) × [21 ^( 5-3) /20^(5-3)]

→ X = (42050-X )× (21/20)²

→ X = (42050 - X) × (441/400 )

→ 400 X = 1,85,44,050 - 441 X

→ 400 X + 441 X = 1,85 , 44 , 050

→ 841 X = 1,85 , 44 , 050

→ X = 1,85 , 44 , 050 / 841

→ X = 22050

So amount of money given to son A is Rs 22050

→ Money given to son B = 42050 - 22050

→ Rs 20,000

Hence , Money given to B is Rs 20k