(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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$A$ sum of $Rs. 2540$ is lent out in two parts,one at $12 \%$ and the other at $12.5 \%$. If the total annual return on the total money invested is $Rs. 312.42$,find the money (in $Rs.$) lent at $12 \% \text{ p.a.}$

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$A$ sum of ₹ $1,550$ is lent out in two parts,one at $8 \%$ and another at $6 \%$. If the total annual income is ₹ $106$,find the money lent at each rate.

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$A$ man invests ₹ $3965$ in the names of his three daughters,Neeta,Sita,and Gita,in such a way that they would receive the same amount after $2, 3,$ and $4$ years. If the rate of interest is $5 \%$ p.a.,then the amount (in ₹) invested for Neeta,Sita,and Gita is:

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The simple interest on a certain sum of money at the rate of $5 \%$ per annum for $8$ years is ₹ $840$. What is the rate of interest per annum for which the same amount of interest can be received on the same sum after $5$ years (in $\%$)?

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The simple interest accrued on a certain principal is ₹ $1200$ in $4$ years at the rate of $8 \%$ per annum. What would be the simple interest (in ₹) accrued on thrice of that principal at the rate of $6 \%$ per annum in $3$ years?

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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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$A$ sum of $Rs. 2540$ is lent out in two parts,one at $12 \%$ and the other at $12.5 \%$. If the total annual return on the total money invested is $Rs. 312.42$,find the money (in $Rs.$) lent at $12 \% \text{ p.a.}$

$A$ sum of ₹ $1,550$ is lent out in two parts,one at $8 \%$ and another at $6 \%$. If the total annual income is ₹ $106$,find the money lent at each rate.

$A$ man invests ₹ $3965$ in the names of his three daughters,Neeta,Sita,and Gita,in such a way that they would receive the same amount after $2, 3,$ and $4$ years. If the rate of interest is $5 \%$ p.a.,then the amount (in ₹) invested for Neeta,Sita,and Gita is:

The simple interest on a certain sum of money at the rate of $5 \%$ per annum for $8$ years is ₹ $840$. What is the rate of interest per annum for which the same amount of interest can be received on the same sum after $5$ years (in $\%$)?

The simple interest accrued on a certain principal is ₹ $1200$ in $4$ years at the rate of $8 \%$ per annum. What would be the simple interest (in ₹) accrued on thrice of that principal at the rate of $6 \%$ per annum in $3$ years?

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