Question

let an amount of rs 432000 is divided among four persons A, B, C and D in the ratio 23/4:11/2:31/2:11/4.find the share of D. class 8 advance maths questions 77 chapter 2.​

Answer 1

Answer:-

Given:-

Amount to be divided = ₹ 4,32,000

Ratio of amount to be divided among A, B , C and D = (23/4) : (11/2) : (31/2) : (11/4).

Method - 1:-

We can find the amount received by D , by dividing the ratio of D with the total sum of the ratios and multiplying it by the total amount.

Total sum of the ratios = (23/4) + (11/2) + (31/2) + (11/4)

= (23 + 22 + 62 + 11)/4

= 118/4

= 59/2

Now;

Amount received by D = { (11/4) / (59/2) } × 432000

= (11)(2)(432000) / (4)(59)

= ₹ 40,271.1

Method - 2:-

Let , the amounts received by A , B , C & D be ₹ 23x/4 ; ₹ 11x/2 ; ₹ 31x/2 & ₹ 11x/4.

We have total amount i.e., ₹ 432000

According to the question;

⟹ 23x/4 + 11x/2 + 31x/2 + 11x/4 = 432000

⟹ (23x + 22x + 62x + 11x) / 4 = 432000

⟹ 118x/4 = 432000

⟹ x = 432000 × 4/118

⟹ x = ₹ 14, 644

Now,

Share of D = 11x/4 = 11(14644)/4 = ₹ 40,271.1

∴ The share of D is ₹ 40,271.1

Answer 2

Answer:

Given :-

• An amount of Rs 432000 is divided among four persons A , B , C and D in the ratio of 23/4 : 11/2 : 31/2 : 11/4.

To Find :-

• What is the share of D.

Solution :-

Let, the amount received be :

$\longmapsto$ $\sf A's\: received =\: \dfrac{23x}{4}$

$\longmapsto$ $\sf B's\: received =\: \dfrac{11x}{2}$

$\longmapsto$ $\sf C's\: received =\: \dfrac{31x}{2}$

$\longmapsto$ $\sf D's\: received =\: \dfrac{11x}{4}$

Given :

• Amount = Rs 432000

According to the question :

$\implies \sf \dfrac{23x}{4} + \dfrac{11x}{2} + \dfrac{31x}{2} + \dfrac{11x}{4} =\: 432000$

$\implies \sf \dfrac{23x + 22x + 62x + 11x}{4} =\: 432000$

$\implies \sf \dfrac{118x}{4} =\: 432000$

By doing cross multiplication we get :

$\implies \sf 118x =\: 4(432000)$

$\implies \sf 118x =\: 1728000$

$\implies \sf x =\: \dfrac{\cancel{1728000}}{\cancel{118}}$

$\implies \sf x \approx 14644.07$

$\implies \sf\bold{\purple{x =\: Rs\: 14644}}$

Hence, the required amount share by A , B , C and D are :

➲ Amount share by A :

↦ $\sf Rs\: \dfrac{23x}{4}$

↦ $\sf Rs\: \dfrac{23(14644)}{4}$

↦ $\sf Rs\: \dfrac{\cancel{336812}}{\cancel{4}}$

➠ $\sf\bold{\red{Rs\: 84203}}$

➲ Amount share by B :

↦ $\sf Rs\: \dfrac{11x}{2}$

↦ $\sf Rs\: \dfrac{11(14644}{2}$

↦ $\sf Rs\: \dfrac{\cancel{161084}}{\cancel{2}}$

➠ $\sf\bold{\red{Rs\: 80542}}$

➲ Amount share by C :

↦ $\sf Rs\: \dfrac{31x}{2}$

↦ $\sf Rs\: \dfrac{31(14644)}{2}$

↦ $\sf Rs\: \dfrac{\cancel{453964}}{\cancel{2}}$

➠ $\sf\bold{\red{Rs\: 226982}}$

➲ Amount share by D :

↦ $\sf Rs\: \dfrac{11x}{4}$

↦ $\sf Rs\: \dfrac{11(14644)}{4}$

↦ $\sf Rs\: \dfrac{\cancel{161084}}{\cancel{4}}$

➠ $\sf\bold{\red{Rs\: 40271}}$

$\therefore$ The amount share by D is Rs 40271 .