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2 votes

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 $?$

- $₹580$
- $₹570$
- $₹560$
- $₹590$

1 vote

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 $: \text{C}$

$$\begin{array}{|c|c|c|}\hline \text{Months} & \text{Rice} & \text{Wheat} \\\hline \text{April} & x & y \\\hline \text{May} & 1.2x & 1.12y \\\hline \end{array}$$

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 $: \text{C}$