Kumar purchased 100 toys of same type. He sells 60% of toys at a gain

1.	Kumar purchased 100 toys of same type. He sells 60% of toys at a gain of 20% and 40% at a gain of 10%. Had he sold all the toys at 12.5% (uniform) profit, he has got Rs. 70 less. Find C.P of each toy (In Rs.)1. 252. 303. 204. 15
Answer» Correct Answer - Option 3 : 20 Given: Total number of toys = 100 Profit earned by selling 60% toys = 20% Profit earned by selling 40% toys = 10% Overall profit percent = 12.5% (uniform) Difference between initial S.P and final S.P = 70 Formula used: Selling price = (100 ± a %)/100 × C.P Where + a% = percent profit, and – a% = percent loss Concept used: Profit and loss is always calculated on C.P Calculation: Let Total C.P of 100 toys be X. C.P of 60 toys = (X/100) × 60 = 3X/5 C.P of 40 toys = (X/100) × 40 = 2X/5 Profit percent, while selling 60 toys = 20% S.P = (100 + 20)/100 × 3X/5 ⇒ 120/100 × 3X/5 ⇒ 18X/25 Similarly, profit percent, while selling 40 toys = 10% S.P = (100 + 10)/100 × 2X/5 ⇒ 11X/25 Total S.P of 100 toys = 18X/25 + 11X/25 = 29X/25 Now, toys are sold at uniform profit at 12.5% Total S.P of toys = (100 + 12.5)/100 × X = 9X/8 Difference between initial and final S.P = 70 ⇒ 18X/25 – 9X/8 = 70 ⇒ 7X/200 = 70 ⇒ X = 2000 Total C.P of 100 toys = X = 2000 C.P of each toy = 2000/100 = 20 ∴ C.P of each toy is Rs. 20.

Kumar purchased 100 toys of same type. He sells 60% of toys at a gain of 20% and 40% at a gain of 10%. Had he sold all the toys at 12.5% (uniform) profit, he has got Rs. 70 less. Find C.P of each toy (In Rs.)1. 252. 303. 204. 15

Answer» Correct Answer - Option 3 : 20

Given:

Total number of toys = 100

Profit earned by selling 60% toys = 20%

Profit earned by selling 40% toys = 10%

Overall profit percent = 12.5% (uniform)

Difference between initial S.P and final S.P = 70

Formula used:

Selling price = (100 ± a %)/100 × C.P

Where + a% = percent profit, and – a% = percent loss

Concept used:

Profit and loss is always calculated on C.P

Calculation:

Let Total C.P of 100 toys be X.

C.P of 60 toys = (X/100) × 60 = 3X/5

C.P of 40 toys = (X/100) × 40 = 2X/5

Profit percent, while selling 60 toys = 20%

S.P = (100 + 20)/100 × 3X/5

⇒ 120/100 × 3X/5

⇒ 18X/25

Similarly, profit percent, while selling 40 toys = 10%

S.P = (100 + 10)/100 × 2X/5

⇒ 11X/25

Total S.P of 100 toys = 18X/25 + 11X/25 = 29X/25

Now, toys are sold at uniform profit at 12.5%

Total S.P of toys = (100 + 12.5)/100 × X = 9X/8

Difference between initial and final S.P = 70

⇒ 18X/25 – 9X/8 = 70

⇒ 7X/200 = 70

⇒ X = 2000

Total C.P of 100 toys = X = 2000

C.P of each toy = 2000/100 = 20

∴ C.P of each toy is Rs. 20.