A and B together have Rs. 6300. If 5/19 of A’s amount is equal to 2/5 of B’s amount, find the amount of B?
Rs. 2500
Let A's amount be x and B's amount be y. According to the problem, x + y = 6300. We are also given that \(\frac{5}{19}\) of A's amount is equal to \(\frac{2}{5}\) of B's amount. This can be represented as:
\(\frac{5}{19}x = \frac{2}{5}y\)
To eliminate the fractions, multiply both sides by 95 (the LCM of 19 and 5):
5x = 38y
Express x in terms of y:
x = \(\frac{38}{5}y\)
Substitute this expression into the equation x + y = 6300:
\(\frac{38}{5}y + y = 6300\)
This simplifies to:
\(\frac{38y + 5y}{5} = 6300\)
\(\frac{43y}{5} = 6300\)
Multiply both sides by 5 to clear the fraction:
43y = 31500
Solving for y gives:
y = \(\frac{31500}{43}\)
Calculating the division gives:
y = 2500
Therefore, the amount of B is Rs. 2500.
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