Question

A invest 3/8 part of total capital for 10 months and rest capital invest by B some month for B go to 4/7 part of total profit for how much time period B invest.​

Answer 1

Gɪᴠᴇɴ :-

• A invest 3/8 part of total capital for 10 months .
• rest capital invest by B for some month .
• B go to 4/7 part of total profit..

Tᴏ Fɪɴᴅ :-

• For How Much Time B Invest ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• The Profit is distributed in The ratio of their capital invested * Time Period.

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, B invest Rest of the capital for x Months.

Than, we have Now :-

→ A capital = (3/8) Part.

→ A time = 10 Months.

→ B capital = 1 - (3/8) = (5/8) Part .

→ B Time = x Months.

→ Profit share of B = (4/7) Part.

→ So, Profit Share of A = 1 - (4/7) = (3/7) Part.

Or,

→ Profit A : Profit B = 3 : 4.

A/q,

→ (3/8) * 10 : (5/8) * x = 3 : 4

→ 30 : 5x = 3 : 4

→ 6 : x = 3 : 4

→ (6/x) = (3/4)

→ x = (6 * 4) / 3

→ x = 8 Months. (Ans.)

Hence, B invested For 8 Months.

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer = 8 months

$\rule{110}1$

$\huge\sf\blue{Given}$

➳ A invests $\sf\dfrac{3}{8}$ part of total capital for 10 months

➳ Then the rest capital is invested by B for some month

➳ B got $\sf\dfrac{4}{7}$ part of total profit

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

✭ The time B invested?

$\rule{110}1$

$\huge\sf\purple{Steps}$

❍ Assume that B invested for the remaining "x months"

So,

☆ A capital = $\sf\dfrac{3}{8}$ part

☆ A time = 10 months

☆ B capital = 1 - $\sf\dfrac{3}{8}$ = $\sf\dfrac{5}{8}$ part

☆ B time = x months

☆ The profit share of B = $\sf\dfrac{4}{7}$ Part

☆ Now with that the profit part of A = 1 - $\sf\dfrac{4}{7}$ = $\sf\dfrac{3}{7}$ Part

☆ Or in other way their shares are of the ratio 3:4

Now,

➝ $\sf\dfrac{3}{8}$ × 10 : $\sf\dfrac{5}{8}$ × x = 3:4

➝ 30:5x = 3:4

➝ 6:x = 3:4

➝ x = $\sf\dfrac{6×4}{3}$

➝ x = $\sf\dfrac{24}{3}$

➝ x = $\sf\orange{8 \: months}$

$\rule{170}3$