Question

Kavya invested amounts in 3 schemes P,Q and Rat simple interest rates of 11% p.a, 13% p.a, and 16% p.a. respectively. If the total interst in 1 year was ₹2,850 and the amount in scheme R was 200% of scheme P and 300% of scheme Q, what was the amount invested in scheme Q ?

• A. ₹3677
• B. ₹2750
• C. ₹3000
• D. ₹3250

Answer 1

Answer:

A. ₹3677

Let's check the given data carefully.

Let the investments be (P), (Q), and (R).

Given:

• $(R = 200\%) of (P \Rightarrow R = 2P).$

• $(R = 300$

Hence,
$P=\frac{R}{2},\qquad Q=\frac{R}{3}.$

The total interest for 1 year is:
$0.11P + 0.13Q + 0.16R = 2850.$

Substitute (P=\frac{R}{2}) and (Q=\frac{R}{3}):
$0.11\left(\frac{R}{2}\right) + 0.13\left(\frac{R}{3}\right) + 0.16R = 2850$

• $0.055R + 0.043333R + 0.16R = 2850$
  
  $0.258333R = 2850$
  

  • $R = \frac{2850}{0.258333} \approx 11032.26$
    

Therefore,
$Q=\frac{R}{3}\approx \frac{11032.26}{3}=3677.42$

Rounded to the nearest rupee:

=₹3677

So the provided answer ₹3677 is correct after rounding.