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Akash, Sameer, and Sid took a house on rent for once a year for Rs.16236. They stayed together for 4 months and then sid left the house. After 5 more months. Sameer also left the house. How much rent should each pay?

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#### Solution

Let ‘R’ be the rent per month to be paid to the landlord.

Given that, Sid left the house after 4 months

∴ Rent paid by Sid = `"R"/3 xx 4 = (4"R")/3`

Sameer left the house after another 5 months,

∴ Rent paid by Sameer = `"R"/2 xx 5 + "R"/3 xx 4`

= `"R"(5/2 + 4/3)`

= `(23"R")/6`

Akash stayed in the house for the entire year.

∴ Rent paid by Akash = `3"R" + "R"/2 xx 5 + "R"/3 xx 4`

= `"R"(3 + 5/2 + 4/3)`

= `(41"R")/6`

∴ The rent paid by the three of them, over that period of one year must be in proportion.

`(41"R")/6.(23"R")/6.(4"R")/3`

i.e. in the proportion

41 : 23 : 8 .....(multiplying throughhout by `6/"R"`)

Let x be the constant of proportionality.

Rent to be paid by Akash = ₹ 41x

Rent to be paid by Sameer = 23x

and rent to be paid by Sid = 8x

The total rent for the house was ₹ 16236.

∴ 41x + 23x + 8x = ₹16236

∴ 72x = 16236

x = 225.5

∴ Akash should pay 41x = `41 xx 225.5`

= ₹ 9245.5

Sameer should pay 23x = 23 × 225.5

= ₹ 5186.5

and Sid should pay 8x = 8 × 225.5 = ₹ 1804

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