Question

An article is listed at ₹ 65. A customer bought this article for ₹ 56.16 and got two successive discounts, the first being $10\%$. What was the other discount rate allowed by the shopkeeper?

• A. $3\%$
• B. $4\%$
• C. $6\%$
• D. $2\%$

Hint:

For two discounts $d_1$ and $d_2$, the net multiplier is $(1-d_1)(1-d_2)$. Equivalently, the combined discount is $1-(1-d_1)(1-d_2)$.

Answer 1

The Correct Option is B

Step 1: Write the successive-discount equation.
Let the second discount be $x\%$. Then \[ \text{Net Price}=\underbrace{₹ 65}_{\text{List}}\times(1-0.10)\times(1-x)=₹ 56.16. \] 

Step 2: Solve for $x$.
$65\times 0.9=58.5$ $\Rightarrow$ $58.5(1-x)=56.16$
$\Rightarrow\ 1-x=\dfrac{56.16}{58.5}=0.96$ (since $58.5\times 0.96=56.16$)
$\Rightarrow\ x=1-0.96=0.04=4\%$.
\[ \boxed{4\%} \]