Question

A sells to b goods at five-thirds the rate of profit at which b has decided to sell it to c. C, on other hand sells it to d at one-third the rate of profit at which b sold it to c. If d gives rs. 2145 to c at 10%, how much did a buy it for ?

Answer 1

Answer: Rs. 1000

Step-by-step explanation:

Step 1:

D gave to C = Rs. 2145

Profit rate = 10%

∴ C.P. of C  

= [100/(100+P)]*S.P  

= [100/100+10]*2145  

= (100/110) * 2145

= Rs. 1950

Step 2:

S.P. of B = C.P. of C = Rs. 1950

It is given that C had sold the goods to D at 1/3rd of profit rate at which B sold it to C

So, 1/3rd of (profit rate for B) = 10%

i.e., profit rate for B = 3 * 10% = 30%

∴ C.P. of B  

= [100/(100+P)]*S.P  

= [100/100+30]*1950

= (100/130) * 1950

= Rs. 1500

Step 3:

Now, S.P. of A = C.P. of B = Rs. 1500

It is given that A had sold the goods to B at 5/3rd of profit rate at which B sold it to C

So, (profit rate for A) = 5/3 * 30% = 50%

∴ C.P. of A  

= [100/(100+P)]*S.P  

= [100/100+150]*1500

= (100/150) * 1500

= Rs. 1000

Thus, A bought the goods for Rs. 1000.

Pictorial representation of the transactions between A, B, C & D is attached below: