Shiva invested an amount of $₹\ 12,000$ at the rate of 10% pa simple interest and another amount at the rate of 20% pa simple interest. The total interest earned at the end of the year on total amount invested became 14% pa. Find the total amount invested.
(A) ₹ 18,000
(B) ₹ 20,0

Question

Shiva invested an amount of $₹\ 12,000$ at the rate of 10% pa simple interest and another amount at the rate of 20% pa simple interest. The total interest earned at the end of the year on total amount invested became 14% pa. Find the total amount invested.
(A) ₹ 18,000
(B) ₹ 20,000
(C) ₹ 24,000
(D) ₹ 26,000

Accepted Answer

> [!TLDR]
> $1200+0.20y=0.14(12000+y)\Rightarrow y=8000$; total $=12000+8000=₹20,000$.

### Step 1 — set up

First part $₹12,000$ at 10%, second part $y$ at 20%. The combined interest equals 14% of the **total** invested:

$$0.10(12000)+0.20y=0.14(12000+y).$$

### Step 2 — expand

$$1200+0.20y=1680+0.14y.$$

### Step 3 — solve for $y$

$$0.06y=480\ \Rightarrow\ y=8000.$$

### Step 4 — total invested

The question asks for the **total** amount, so add both parts:

$$12000+8000=₹20,000.$$ …

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