Question

A labourer was engaged for 30 days on the condition that he will pe paid ₹ 2.50 every day he works and will be fined ₹ 1 for every day he is absent. he earned₹ 47 in all. find how many days did he work ?

Answer 1

sᴏʟᴜᴛɪᴏɴ

suppose that the labourer works for x days and is absent for y days.

∴ x+y = 30

For working x days, he earns ₹ (x × 2.50) = ₹ 5/2 x

For being absent for y days, he is fined ₹ (y × 1) = ₹ y

∴ By the question, 5/2 x - y = 47

Adding (1) and (2),

x + 5/2 x = 30 + 47

⇒7/2x = 77

x = 77 × 2/7 = 22

$<b><i> hence the labourer worked for 20 days.$

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Answer 2

let a = days absent
let w = days worked
:
a + w = 30
and
-10a + 80w = 1860
:
multiply the first equation by 10, add to the 2nd equation
10a + 10w = 300
-10a+ 80w =1860
------------------addition eliminates a, find w
0 + 90w = 2160
w = 2160/90
w = 24 days worked
:
:
Check this, 30-24 = 6 days absent
24*80 = 1920
6*10 = - 60
--------------
amt paid 1860

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