P began a business with Rs. 45,000 and Q joined with Rs. 30,000 after some…
2024
P began a business with Rs. 45,000 and Q joined with Rs. 30,000 after some time. If the profit at the end of the year were divided among them in the ratio 2 : 1, when did Q join?
- A.
after 3 months
- B.
after 4 months
- C.
after 5 months
- D.
after 6 months
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Let Q join after x months. So, P invested for 12 months and Q invested for (12 - x) months.
The profit ratio is given as 2 : 1, which is based on the product of investment and time.
So, (45000 × 12) / (30000 × (12 - x)) = 2 / 1
Simplify: (540000) / (30000 × (12 - x)) = 2
540000 = 2 × 30000 × (12 - x)
540000 = 60000 × (12 - x)
12 - x = 540000 / 60000 = 9
x = 12 - 9 = 3
So, Q joined after 3 months.
हिन्दी उत्तर:
माना Q, x महीने बाद शामिल हुआ। इसलिए, P ने 12 महीने के लिए निवेश किया और Q ने (12 - x) महीने के लिए निवेश किया।
लाभ का अनुपात 2 : 1 दिया गया है, जो निवेश और समय के गुणनफल पर आधारित है।
इसलिए, (45000 × 12) / (30000 × (12 - x)) = 2 / 1
सरल करने पर: (540000) / (30000 × (12 - x)) = 2
540000 = 2 × 30000 × (12 - x)
540000 = 60000 × (12 - x)
12 - x = 540000 / 60000 = 9
x = 12 - 9 = 3
इसलिए, Q 3 महीने बाद शामिल हुआ।