Question

Raju sells cement at a profit of 10%. Had he bought at 10% less and sold it for Rs. 20 less, he would have gained 20 %. Then what is the cost price of the cement?​

Answer 1

Answer:

CP = Rs. 1000

Step-by-step explanation:

Given:-

Raju sells cement at a profit of 10%. Had he bought at 10% less and sold it for Rs. 20 less, he would have gained 20 %.

To Find:-

Cost price of the cement.

Solution:-

♦ Let CP be Rs.x

Gain% = 10%

So, Gain = 10% of x = x/10

So, SP = CP + Gain

→x+x/10

→10x+x/10

→Rs. 11x/10

Now, New CP = x - 10% of x

→x-x/10

→9x/10

Now, Gain = 20%

So,

New SP =

$\longrightarrow \rm \bigg \{ \frac{(100 + gain\% \times \: CP }{100} \bigg \} \\ \longrightarrow \rm \frac{120}{100} \times \frac{9x}{10} \\ \longrightarrow \rm \frac{108x}{100}$

It is given that SP become 20 less

So,

$\leadsto \rm \: \frac{11x}{10} - \frac{108x}{100} = 20 \\ \leadsto \rm110x - 108x = 2000 \\ \leadsto \rm2x = 2000 \\ \leadsto \rm \: x = \cancel \frac{2000}{2} \\ \leadsto \rm \: x = 1000$

So, CP = Rs. 1000

Answer 2

Solution :

We have to find the cost price of the cement here. Let us assume that the cost price of the cement is Rs. x [ For a certain amount, not specified ]

He sells the cement at a profit of 10%.

Value of sp of cement > 110% of x > 1.1 x

Now if he had bought at 10% less

CP of cement = 90% of x = 0.9x

SP = 1.1x - 20

Gain = SP - CP = 1.1x - 20 - 0.9x

> Gain = 0.2 x - 20

Gain percentage :

> [ Gain ]/[ CP ] × 100 % = 20% of x

> ( 0.2x - 20)/(0.9x) × 100 = x/5

> (2x - 200)/9x × 1000 = x/5

This will result in a quadratic equation and the positive value of x is 1000.

Therefore the cost price of the cement is Rs. 1000( for the specified amount) .

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