Question

Raju is engaged to do a work on a condition that he will receive Rs.900 for each day he works and he will be fined Rs.200 for each day he is absent. The ratio of the no of days he is present and absent is 3:1.If he received a total amount of Rs 7500 in all find how many days he was absent?

Answer 1

Given :

• Raju receive ₹900 for each day he worked
• Fine , if he's absent = ₹200
• Present to absent ratio = 3:1
• Total amount received = ₹7500

To find :

Number of days he was absent

Let :

• Number of days he was present = x
• Number of days he was absent = y

Solution :

Given that,

Number of days he was Present : Number of days he was absent = 3:1

$\sf \: x : y = 3 : 1 \\ \\ \sf \implies \: \dfrac{x}{y} = \dfrac{3}{1} \\ \\ \sf \implies \: x = 3 y \: .........equation \: 1$

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Amount he receive for number of days he was present = Number of days he was present × Amount per day

➝ Amount he receive for number of days he was present = 900x

Fine for number of days he was absent = Number of days he was absent × fine per day

➝ Fine for number of days he was absent = 200y

Therefore,

Total amount he received = Amount received - Fine

➝ 7500 = 900x - 200y

On putting value of x from equation 1, we get;

➝ 7500 = 900(3y) - 200y

➝ 7500 = 2700y - 200y

➝ 7500 = 2500y

➝ y = 7500 ÷ 2500

➝ y = 3

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ANSWER :

Number of days he was absent = 3