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. - Mathematics and Statistics


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?



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.


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

Concept: Partnership
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Chapter 9: Commercial Mathematics - Miscellaneous Exercise 9 [Page 144]


Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 9 Commercial Mathematics
Miscellaneous Exercise 9 | Q 16 | Page 144


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