Question

Instead of dividing rupees 117 among P,q,r in the ratio 1/2:1/3:1/4: by mistake it was divided in the ratio 2:3:4. Who gained in the transaction

Answer 1

Step 1 : Define x

Given, by mistakely ₹ 117 was divided in the ratio 2 : 3 : 4 among P, Q and R

So, let share of P be 2x, share of Q be 3x and R be 4x

Let us take total ₹117 as the sum

Step 2 : Find the value of x

2x + 3x + 4x = 117

➾ 9x = 117

➾ x = $\dfrac{117}{9}$

➾ x = 13

Step 3 : Find the share of each

Share of P ➾ 2x

➾ 2 × 13

➾ ₹26

Share of Q ➾ 3x

➾ 3 × 13

➾ ₹39

Share of R ➾ 4x

➾ 4 × 13

➾ ₹52

∴ R's transaction is more which is ₹52

Answer 2

Heya !

Here's your answer !!

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GIVEN THAT :

Amount of money = Rs. 117


CASE 1 :

Amount of money to be divided in the ratio among P, Q, and R = 1/2 : 1/3 : 1/4

CASE 2 :

But, instead it was divided in the ratio =
2 : 3 : 4


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TO FIND :

Who gained in the transaction = ?


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SOLUTION :


CASE 1

Le the amount divided be 1x/2, 1x/3 and 1x/4


THE EQUATION FORMED :


1x/2 + 1x/3 + 1x/4 = 117

=> ( 6x + 4x + 3x )/12 = 117

=> x = 117 × 12/13

=> x = 108

P's share = 108/2 = Rs. 54

Q's share = 108/3 = Rs. 36

R's share = 108/4 = Rs. 27


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CASE 2 :

Let the money divided be 2a, 3a and 4a

THE EQUATION FORMED :

2a + 3a + 4a = 117

=> a = 117/9

=> a = 13

P's share = 2 × 13 = Rs. 26

Q's share = 3 × 13 = Rs. 39

R's share = 4 × 13 = Rs. 52


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From Case 1 and Case 2, we get :

Q and R are benefited, but

ANS ) R gained the most in the Transaction.


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THANKS !!