31. A shopkeeper sold two fans for * 1140 each. On one he gains 14%, while on the other he

loses 5%. Calculate his gain or loss per cent in the whole transaction.

31. A shopkeeper sold two fans for * 1140 each. On one he gains 14%, while on the other he

loses 5%. Calculate his gain

By Brielle

Given :To find :Solution :Cost Price of Fan one = [tex]\sf \dfrac{100}{100 + profit \%} \times S.P[/tex]

= [tex]\sf \dfrac{100}{100 + 14} \times 1140[/tex]

= [tex]\sf \dfrac{100}{114} \times 1140[/tex]

= [tex]\sf \dfrac{114000}{114}[/tex]

= 1000

Cost Price of Fan two = [tex]\sf \dfrac{100}{100 – loss \%} \times S.P[/tex]

= [tex]\sf \dfrac{100}{100 -5} \times 1140[/tex]

= [tex]\sf \dfrac{100}{95} \times 1140[/tex]

= [tex]\sf \dfrac{114000}{95}[/tex]

= 1200

Let’s find the Total Selling Price and Cost price,

= 2280

= 2200

Since, S.P > C.P [Hence, it is Profit.]

Profit = S.P – C.P

= 2280 – 2200

= 80

Now,

Profit% = [tex]\sf \dfrac{Profit}{C.P} \times 100[/tex]

= [tex]\sf \dfrac{80}{2200} \times 100[/tex]

= [tex]\sf \dfrac{8000}{2200}[/tex]

= 3.6%

Therefore, the Profit% of the fan is

3.6%.