(c) 14
Suppose I have x, one-rupee coins and y, 20 – paise coins.
x × 1 + y × 0.2 = 14.40 \(\Rightarrow\) x + 0.2y = 14.4 …(i)
After shopping, I had y one-rupee coins and x 20-paise coins.
Also, x × 0.2 + y × 1 = \(\frac{1}{3}\) x 14.4
\(\Rightarrow\) 0.2x + y = 4.8 ........(ii)
[Note: To solve the equations of the form ax + by = c and bx + ay = d, where a \(\ne\) b, we can use the following method also.]
Adding eqn (i) and (ii), we get
1.2 x + 1.2 y = 19.2 \(\Rightarrow\)x + y = \(\frac{19.2}{1.2}\)= 16 .........(iii)
and subtracting eqn (ii) from eqn (i), we get
– 0.8x + 0.8y = –9.6 \(\Rightarrow\) x – y = 12 ..........(iv)
Now adding (iii) and (iv), we get
2x = 28 \(\Rightarrow\) x = 14.