A man, his wife and daughter worked in a garden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to woman is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings are mounted to Tk. 105, then find the daily wage of the daughter.

Question: A man, his wife and daughter worked in a garden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to woman is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings are mounted to Tk. 105, then find the daily wage of the daughter.

Solution:
Man : Woman = 5 : 4
Man : Daughter = 5 : 3
∴ Man : Woman : Daughter = 5 : 4 : 3

মনে করি,
পুরুষের দৈনিক মজুরি = 5x টাকা
স্ত্রীর দৈনিক মজুরি = 4x টাকা
কন্যার দৈনিক মজুরি = 3x টাকা

প্রশ্নমতে,
(পুরুষের কাজের দিন × মজুরি) + (স্ত্রীর কাজের দিন × মজুরি) + (কন্যার কাজের দিন × মজুরি) = মোট আয়
⇒ (3 × 5x) + (2 × 4x) + (4 × 3x) = 105
⇒ 15x + 8x + 12x = 105
⇒ 35x = 105
⇒ x = 105/35
⇒ x = 3

কন্যার দৈনিক মজুরি = 3x = 3 × 3 = 9 টাকা।

সঠিক উত্তর: ক) Tk. 9