Question

In simple interest if the principal is `2,000 and the Rate and time are the Roots of the
equation x2 – 11x + 30 = 0 then the simple interest is _________
(a) `500 (b) `600
(c) `700 (d) `800

Answer 1

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Answer 2

Answer:

Option (b) is the correct answer.

Step-by-step explanation:

Simple interest, S.I = $\frac{P \cdot R\cdot T}{100}$

where $P$ = Principal, $R$ = rate per year and $T$ = time (in years)

Given: $P$ = Rs.2000

Now,

Consider the equation as follows:

$x^2-11x+30=0$

Using middle term splitting method, compute the roots of the equation as follows:

⇒ $x^2-5x-6x+30=0$

⇒ $x(x-5)-6(x-5)=0$

⇒ $(x-5)(x-6)=0$

⇒ $x=5$ or $x=6$

Take $R$ = 5 and $T$ = 6 years. Then,

S.I = $\frac{2000 \cdot 5\cdot 6}{100}$ (Given: $P$ = Rs.2000)

    = 20 × 5 × 6

    = 600

Observe that the value of simple interest remains unaffected for $T$ = 5 years and $R$ = 6.

Thus, the simple interest is Rs.600.

Therefore, option (b) is correct.

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