I had Rs 14.40 in one-rupee coins and 20 paise coins when I went out s

1.	I had Rs 14.40 in one-rupee coins and 20 paise coins when I went out shopping. When I returned, I had as many one rupee coins as I originally had 20 paise coins and as many 20 paise coins as I originally had one rupee coins. Briefly, I came back with about one-third of what I had started out with. How many one-rupee coins did I have initially ? (a) 10 (b) 12 (c) 14 (d) 16
Answer» (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.

I had Rs 14.40 in one-rupee coins and 20 paise coins when I went out shopping. When I returned, I had as many one rupee coins as I originally had 20 paise coins and as many 20 paise coins as I originally had one rupee coins. Briefly, I came back with about one-third of what I had started out with. How many one-rupee coins did I have initially ? (a) 10 (b) 12 (c) 14 (d) 16

Answer»

(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.