X lent ₹6,000 to Y for 3 years and ₹4,000 to Z for 2 years, both at the same simple interest rate. In total, he received ₹2,000 as interest from both. What is the rate of interest per annum(nearest integer)?

The correct option is 8%.

Let the rate of interest per annum be $R$%.

The formula for Simple Interest ($SI$) is given by:

$SI=\frac{P\times R\times T}{100}$

where:
$P$ = Principal amount
$R$ = Rate of interest per annum
$T$ = Time period in years

Step 1: Calculate the interest received from Y.
Principal ($P_1$) = ₹6,000
Time ($T_1$) = 3 years

$S{I}_1=\frac{6000\times R\times 3}{100}=180R$

Step 2: Calculate the interest received from Z.
Principal ($P_2$) = ₹4,000
Time ($T_2$) = 2 years

$S{I}_2=\frac{4000\times R\times 2}{100}=80R$

Step 3: Calculate the total interest received.
Total Interest = $S{I}_1+S{I}_2$

We are given that the total interest received from both Y and Z is ₹2,000.

$180R+80R=2000$

$260R=2000$

$R=\frac{2000}{260}=\frac{100}{13}\approx 7.69\%$

Rounding off to the nearest integer, we get:

$R\approx 8\%$

Therefore, the rate of interest per annum is 8%.