Raju sold a watch to Sanjeev at a 20% gain; Sanjeev sold it to Mukesh at a loss of 10%. If Mukesh bought it for ₹4,860, then at what price did Raju purchase it?

Correct option is B

Given:

Raju sold watch to Sanjeev at 20% profit

Sanjeev sold watch to Mukesh at 10% loss

Mukesh bought watch for ₹4860

Formula Used:

Profit = SP - CP

Profit Percentage = $$\frac{Profit}{Cost\ Price} \times 100$$​​

Solution:

Let the Cost Price of watch for Raju be $$x$$​

Then Raju sold watch to Sanjeev at 20% gain

Selling Price of watch for Raju = $$x + 20\% \ of \ x = 1.2x$$​​

But Selling Price is equal to cost Price for Sanjeev

So, Sanjeev bought watch for Rs $$1.2x$$​​

Sanjeev sold the watch at 10% loss

SP for Sanjeev = $$1.2x - 10\% \ of \ 1.2x$$​

= $$1.2x - 0.12x = 1.08x$$​​

But SP for Sanjeev is equal to CP for Mukesh = $$1.08x$$​​

And Mukesh bought watch for ₹4860

So 1.08x = 4860

x = $$\frac{4860}{1.08} = ₹ 4500$$​​

Alternative Method:

Successive Percentage formula:$$x + y + \frac{xy}{100}$$​​

Putting the values as 20% and -10%

= $$20 -10 + \frac{(20)(-10)}{100}$$​​

= 10 - 2 = 8%

So the SP is 100 + 8 = 108%

Here

108 = 4860

1 =$$\frac{4860}{108}$$​​

​$$100 =\frac{4860}{108} \times 100 = ₹4500$$​​

Alternative Method 2:

​$$SP = CP (\frac {100+Profit}{100})(\frac{100-Loss}{100})$$​​

​$$4860 = CP (\frac {100+20}{100})(\frac{100-10}{100})$$​​

​$$CP = 4860 \times (\frac{100}{120})(\frac{100}{90})$$​​

​$$CP =₹4500$$​​