Question

1700 rupees are to be distributed among three people A, B and C. A got double of B and the five times of C. Then how much money does B get?
A) Rs.300
B) Rs.400
C) Rs.500
D) Rs.700

Answer 1

Hint:
Here, we have given the Rs1700 and we have distributed them in such a way that A got double of B and the five times of C. So, we will consider A as x, B as y and C as z and then apply a given condition.

Complete step by step solution:
Here, the three people A, B and C and consider the amount of money given to them as x, y and z.
Now, A has a x rupees, B has a y rupees and C has a z rupees.
A got the double of B.
\[\therefore x = 2y\] equation (1)
Also, A got the fives times of C
 $\therefore x = 5z$ Equation (2)
The sum of the total amount which is to be distributed is 1700 rupees.
 $
  \therefore x + y + z = 1700 \\
  \therefore x + \dfrac{x}{2} + \dfrac{x}{5} = 1700
 $
Putting the equation (1) and the equation (2)
 $
  \therefore \dfrac{{10x}}{{10}} + \dfrac{{5x}}{{10}} + \dfrac{{2x}}{{10}} = 1700 \\
  \therefore 10x + 5x + 2x = 17000 \\
  \therefore 17x = 17000 \\
  \therefore x = \dfrac{{17000}}{{17}} \\
  \therefore x = 1000
 $
Therefore, the amount that A get =x
$\Rightarrow 1000 \text{ Rs}$
Now, the amount that B get
 $
  y = \dfrac{x}{2} \\
  y = \dfrac{{1000}}{2}
 $
 $\therefore y = 500$ Rs
And the amount that C get
$\therefore z = 200$ Rs

Therefore, the A got 1000 Rs, B got 500 Rs and C got 200 Rs.

Note:
Here, we have the relation of A with the B and C in which we have given that A is got 2 times the B and 5 times of C. i.e. A is equal to the 5 times of B (we have to return the $A = 5B$ not $B = 5A$)