Question

lady went to the market with a few 1 Rupee notes and a few 20 paise coins. when she returned she had as many 1 rupee notes as she originally had 20 paise coins and vice versa. She actually came back with about two third of what she had gone with. How much could she spend in the market, if number of 20 paise coins lies between 45 to 50.

Answer 1

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Answer 2

Answer: 100.8 rupees

Step-by-step explanation:

Let she has x coins of 1  rupees and y coins of 20 paise,

Hence, the total amount she has initially = ( x + 0.2 y ) rupees,

According to the question,

The number of 20 paise coins after shopping = x

And, number of 1 rupee coins after shopping = y

Hence, the amount after shopping = ( 0.2 x + y ) rupees,

Again according to the question,

2/3 of  ( x + 0.2 y ) = ( 0.2 x + y )

$\implies \frac{2}{3}\times (x+0.2 y) = 0.2 x + y$

$\implies 2x + 0.4 y = 0.6 x + 3 y$

$\implies 1.4 x = 2.6 y$

$\implies \frac{x}{y}=\frac{2.6}{1.4}=\frac{13}{7}$

Since, If  if number of 20 paise coins lies between 45 to 50.

Thus, the possible value of y = 49,

Thus, x = 91

Hence, the initial amount =  ( x + 0.2 y ) rupees = 91 + 9.8 = 100.8 rupees