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In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent $₹150$ more due to price increase of rice and wheat by $20\%$ and $12\%,$ respectively. If John had spent $₹450$ on rice in April, then how much did he spend on wheat in May $?$

1. $₹580$
2. $₹570$
3. $₹560$
4. $₹590$

## 1 Answer

Let the price of rice in April be $₹ \; x,$ and the price of wheat in April be $₹ \; y.$

$$\begin{array}{|c|c|c|}\hline \text{Months} & \text{Rice} & \text{Wheat} \\\hline \text{April} & x & y \\\hline \text{May} & 1.2x & 1.12y \\\hline \end{array}$$
Now, $1 . 2x + 1 . 12y = 150 + x + y$

$\Rightarrow \frac{12}{10}(450) + 1. 12y = 150 + 450 + y$

$\Rightarrow 540 + 1 . 12y = 600 + y$

$\Rightarrow 1 . 12y – y = 600 – 540$

$\Rightarrow \frac{12}{100}y = 60$

$\Rightarrow 12y = 60 \times 100$

$\Rightarrow \boxed{ y = 500}$

So, money spend on wheat in May $= 1 . 12y = \frac{112}{100} \times 500 = ₹560$

$\therefore$ The money spends on the wheat in May is $₹560.$

Correct Answer $: \text{C}$
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