(A) Let the time after which the amounts are equal be $N$ years.Amount of debt for $A = P + \text{Simple Interest} = P + \frac{P \times x \times N}{10

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$100\left(\frac{Q-P}{Px-Qy}\right)$ years

(A) Let the time after which the amounts are equal be $N$ years.Amount of debt for $A = P + \text{Simple Interest} = P + \frac{P \times x \times N}{100}$.Amount of debt for $B = Q + \text{Simple Interest} = Q + \frac{Q \times y \times N}{100}$.Since the amounts are equal,we set them equal to each other:$P + \frac{PxN}{100} = Q + \frac{QyN}{100}$.Rearranging the terms to solve for $N$:$\frac{PxN}{100} - \frac{QyN}{100} = Q - P$.$N \left(\frac{Px - Qy}{100}\right) = Q - P$.$N = 100 \left(\frac{Q - P}{Px - Qy}\right)$ years.

Competitive Quantitative Aptitude Interest Simple Interest

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If $A$ borrowed $₹P$ at $x\%$ and $B$ borrowed $₹Q$ $(Q > P)$ at $y\%$ per annum at simple interest at the same time,then the amount of their debts will be equal after:

A
$100\left(\frac{Q-P}{Px-Qy}\right)$ years
B
$100\left(\frac{Px-Qy}{Q-P}\right)$ years
C
$100\left(\frac{Px-Qy}{P-Q}\right)$ years
D
$100\left(\frac{P-Q}{Px-Qy}\right)$ years

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Income of Hemant was Rs. $4000$. In the first $2$ years,his income decreased by $10\%$ and $5\%$ respectively,but in the third year,the income increased by $15\%$. What was his income (in Rs.) at the end of the third year?

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If $A$ borrowed $₹P$ at $x\%$ and $B$ borrowed $₹Q$ $(Q > P)$ at $y\%$ per annum at simple interest at the same time,then the amount of their debts will be equal after:

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Income of Hemant was Rs. $4000$. In the first $2$ years,his income decreased by $10\%$ and $5\%$ respectively,but in the third year,the income increased by $15\%$. What was his income (in Rs.) at the end of the third year?

Shruti borrowed $Rs. 2500$ from her two friends. For one loan she paid $8 \%$ $p.a.$ and for the other $6 \%$ $p.a.$ simple interest. If she paid $Rs. 180$ as total interest for one year,how much did she borrow (in $Rs.$) at $8 \%$ $p.a.?$

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