Algebra
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Q.

$A,B,C$ and $D$ each had some money. $D$ doubled the amounts with the others. $C$ then doubled the amounts with the others. $B$ then doubled the amounts with the others. $A$ then doubled the amounts with the others. At this stage, each of them has Rs 80. Find the initial amount with $C$ (in Rs).

 A.

75

 B.

80

 C.

95

 D.

85

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Solution:
Option(D) is correct

Before doubling, the amounts $B,C$ and $D$, each of them must have had

\(=\dfrac{80}{2}\)

\(=40\)

$A$ must have then had Rs 80+ Rs 120 = Rs 200. 

Similarly, we can work out the amounts with each of them before the other doubled the amounts. 

The results are summarized below:

Finally--------> $A(80), B(80), C(80), D(80)$

Before $A$ doubles --------> $A(200), B(40), C(40), D(40)$

Before $B$ doubles --------> $A(100), B(180), C(20), D(20)$

Before $C$ doubles --------> $A(50), B(90), C(170), D(10)$

Before $D$ doubles --------> $A(25), B(45), C(85), D(165)$


(6) Comment(s)


Vivek
 ()

Visualize apurva's method with abhishek's table.. u will get it


Harshita Singh
 ()

Thanks dude!

this trick worked!


Apurva
 ()

If we start from given information then:

At step 1, all are having 80...means just before it in step 2, A helped others to make their money double. So, in step 2, deduct half of B, C, D and add it to A. At step 3, B helped others to make their money double, so from step 2, deduct half of A, C, D and add it to B.

Do similar thing for C and D till end.

A B C D

80 80 80 80



Abhishek
 ()

Do it in the reverse order

$C$ has Rs 85.

Starting from the last stage, each has got Rs 80.

ABCD
80808080
200404040
1001802020
509017010
254585165


Raju
 ()

Please make me understand the question...



Jayanth
 ()

Dear All,

Any other alternative to solve this problem?