Question

A Started a business with Rs. 4500 and after some time B Joined A with Rs. 5400. The ratio of their profits at the end of a year is 2:1. When did B Join? {HOTS} ​

Answer 1

Gɪᴠᴇɴ :-

• A started with Rs.4500 for 1 year.
• B joined joined after some Time with Rs.5400 .
• Ratio of their profits at the end of a year is 2:1.

Tᴏ Fɪɴᴅ :-

• When did B Join ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• Ratio of Share is Distributed Among Ratio of their sum Multiply by Their Time..

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, B joined After x Months , after A joined .

So,

→ B did Business for = (12 - x) Months.

Now,

→ A's share * A Time : B's share * B Time = 2 : 1

Putting values now we get :-

→ (4500 * 12) : [ 5400 * (12 - x) ] = 2 : 1

→ (4500 * 12) / [ 5400 * (12 - x) ] = 2/1

→ 45 * 12/ 54(12 - x) = 2/1

→ 5 * 12 /6(12 - x) = 2/1

→ 10/ (12 - x) = 2/1

→ 24 - 2x = 10

→ 2x = 24 - 10

→ 2x = 14

→ x = 7 Months. (Ans.)

Hence, we can conclude That, B joined after 7 months of A.

Answer 2

Given :-

• A started a business with ₹ 4500.

• B joined A with ₹ 5400.

• The ratio of their profits at the end of a year is 2 : 1.

To find :-

When did B join.

Solution :-

Let A had begun his business for 1 year. Then according to the given conditions, B joined after some months when A joined.

This means, A ran his business for 12 months.

And B joined with A and ran the business for (12 - n) months.

(Here, 'n' is the months after which B joined)

Now, A/q,

A's share * A's time / B's share * B's time = 2/1

⇒ A's share * A's time : B's share * B's time = 2 : 1

⇒ 4500*12 / 5400(12 - n) = 2/1

⇒ 45*12 / 54(12 - n) = 2/1

⇒ 45*12 : 54(12 - n) = 2/1

⇒ 540 / 648 - 54n = 2/1

⇒ 2(648 - 54n) = 540

⇒ 648 - 54n = 270

⇒ 54n = 648 - 270

⇒ 54n = 378

⇒ n = 7

∴ So, B joined with A after 7 months.