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Rs 3500 is to be shared among three people so that the first person gets 50% of the second, who in turn gets 50% of the third. How much will each of them get? - Mathematics

Numerical

Rs 3500 is to be shared among three people so that the first person gets 50% of the second, who in turn gets 50% of the third. How much will each of them get?

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Solution

Let x, y and z be the amounts received by the first, second and the third person, respectively.
We have: 
x = 50 % of y 
\[ = \frac{50}{100}y = \frac{1}{2}y\]
\[ \therefore y = 2x\]
Again, y = 50 % of z
\[ = \frac{1}{2}z\]
\[ \therefore z = 2y\]
\[ = 2\left( 2x \right)\]
\[ = 4x\]
Also, x + y + z = 3500
Substituting the values of z and y, we get: 
\[x + 2x + 4x = 3500\]
\[ \Rightarrow 7x = 3500\]
\[ \Rightarrow x = 500\]
\[ \therefore y = 2x = 2\left( 500 \right)\]
\[ = 1000\]
\[ \therefore z = 4x = 4\left( 500 \right)\]
\[ = 2000\]
Thus, the amounts received by the first, second and the third person are Rs 500, Rs 1000 and Rs 2000, respectively.

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 12 Percentage
Exercise 12.2 | Q 26 | Page 10
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