Question

What is the sum (in Rs) which when divided among A, B, C, D in the proportion 2:35:8 provides Rs 8420
less to D than what it provides to him when the proportion is?

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Answer 1

Given :- what is the sum (in Rs) which when divided among A, B, C, D in the proportion 2:3:5:8 provides Rs 8420 less to D the what it provides to him when the proportion is 1/2:1/3:1/5:1/8 ?

Solution :

Let us assume that, total sum is Rs.x.

Than,

→ share of D when divide in proportion 2:3:5:8 is = 8/(2 +3 + 5 + 8) of x = (8/18) of x = Rs.(4x/ 9)

now, Ratio in second time :-

→ A:B:C:D=1/2:1/3: 1/5: 1/8

Taking LCM of denominators ,

→ A:B:C:D=(60: 40: 24:15) / 120 = 60: 40: 24:15.

So,

→ Share of D when divided in proportion 60 : 40 : 24 : 15 = 15/(60 + 40 + 24 + 15) of x = (15x/139)

now, given that, he gets Rs.8420 less in second share.

Therefore,

→ (4x/9) - (15x/139) = 8420

→ (139*4x - 135x) /1251 = 8420

→ 556x - 135x = 8420 * 1251

→ 421x = 8420 * 1251

dividing both sides by 421,

→ x = 20* 1251

→ x = Rs.25,020 (Ans.)

Hence the required sum is Rs.25,020.

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