**Maths Shortcuts and Mind Tricks To Solve Partnership Related Problems**

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Q.) Let A and B started a business with initial investments in the
ratio 7:18 and let their annual profits were in the ratio 7:9. If A invested
the money for 10 months then find for how many months did B invested his money?

Shortcut method:

We have Given:

Ratio of
Amount Invested by A and B=

**7:18**
Profit Ratio
of A and B=

**7:9**
A invested
the money for

**10 months**
Let

**x**be the no. of months**invested by B.****To solve the above question we will use the following Formula:**

Now Substitute the given values in the above formula,we get

After Simplify the above equation, we get x = 5.

*Therefore, B has invested the amount for 5 months.*
Q) If A and B started a business with initial investments in the
ratio 8 : 4 and their annual profits were in the ratio 6:4 & Let B invested
the money for 8 months then find for how many months did A invested his money?

Solution:

Ratio of Amount Invested by A and B =

**8:4**
Profit Ratio of A and B =

**6:4**
B invested the money for

**8 months**
Let

**x**be the no. of months**invested by A.****To solve the above question we will use the following Formula:**

By Substituting the given values in the above formula, we get

(8 × 𝑥)/ (4 × 8) = 6/4

After Simplify the above equation, we get x = 6.

*Therefore, A has invested the amount for 6 months.*
Thank You !! J

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