Question

Hari bought 20 kg of rice at ₹ 36 per kg and 25 kg of rice at ₹32 per kg. He mixed the two varieties and sold the mixture at ₹ 38 per kg. Find his gain per cent in whole transaction​.

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Answer 1

Required Answer:

◆ Calculating cost price:

In first part:

• Amount of rice → 20 kg
• Cost price of 1 kg of rice → ₹36

$\rm { \therefore Cost \: price \: of \: 20 \: kg \: of \: rice:– }$

→ ₹ ( 36 × 20 )

→ ₹ 720

In second part:

• Amount of rice → 25 kg
• Cost price of 1 kg of rice → ₹32

$\rm { \therefore Cost \: price \: of \: 25 \: kg \: of \: rice:– }$

→ ₹ ( 25 × 32 )

→ ₹ 800

Total cost price → ₹ (720 + 800)

$\boxed { \rm \pink { \longrightarrow Total \: C.P = Rs \: 1520 }}$

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◆ Calculating selling price:

→ Since, he mixed the two varieties and sold the mixture. So,

• Total amount of rice = ( 20 + 25 ) kg

→ Total amount of rice = 45 kg

• Selling price of 1 kg of rice → ₹38

$\rm { \therefore Selling \: price \: of \: 45 \: kg \: of \: rice:– }$

→ ₹ ( 45 × 38 )

→ ₹ 1710

$\boxed { \rm \pink { \longrightarrow Total \: S.P = Rs \: 1710 }}$

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◆ Calculating gain:

• Gain = S.P – C.P

→ Gain = ₹ ( 1710 – 1520 )

→ Gain = ₹ 190

$\boxed { \rm \pink { \longrightarrow Gai = Rs \: 190 }}$

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◆ Calculating gain %:

We know that,

• Gain % = $\rm {\dfrac{Gain}{C.P} \times 100}$ %

→ Gain % = $\rm {\dfrac{190}{1520} \times 100}$ %

→ Gain % = $\rm {\dfrac{190 \times 100}{1520} }$ %

→ Gain % = $\rm {\dfrac{19000}{1520} }$ %

→ Gain % = $\rm {\dfrac{1900}{152} }$ %

→ Gain % = $\rm {\dfrac{950}{76} }$ %

→ Gain % = $\rm {\dfrac{475}{38} }$ %

→ Gain % = $\rm {\dfrac{25}{2} }$ %

$\boxed { \rm \pink { \longrightarrow Gain \%=\dfrac{25}{2} \%}}$

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Answer 2

Question :-

• Hari bought 20 kg of rice at ₹ 36 per kg and 25 kg of rice at ₹32 per kg. He mixed the two varieties and sold the mixture at ₹ 38 per kg. Find his gain per cent in whole transaction.

Answer

Given :-

• Hari bought 20 kg of rice at ₹ 36 per kg and 25 kg of rice at ₹32 per kg. He mixed the two varieties and sold the mixture at ₹ 38 per kg.

To Find :-

• Gain %

Formula used :-

Gain = Selling Price - Cost Price

$\bf \:Gain\% = \dfrac{Gain}{Cost Price } \times 100\%$

Solution :-

Cost Price of 20 kg of rice at ₹36 per kg = 20 × 36 = ₹720

Cost Price of 25 kg of rice at ₹32 per kg = 25 × 32 = ₹800

⇛ So, Cost Price of 45 kg of rice = 800 + 720 = ₹1520

Selling Price of 1 kg of rice = ₹ 38

⇛Selling price of 45 kg of rice = 45 × 38 = ₹ 1710

So, we concluded that

Selling Price > Cost Price

⇛ There is gain in this transaction.

⇛ Gain = Selling Price- Cost Price

⇛ Gain = 1710 - 1520 = ₹ 190

$\bf\implies \:Gain\% = \dfrac{Gain}{Cost \: Price } \times 1 00\%$

On substituting the values of gain and Cost Price, we get

$\bf\implies \:Gain\% = \dfrac{190}{1520} \times 100\% = 12.5\%$

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Some related formulae:

Gain = S.P – C.P

Loss = C.P – S.P

$\rm { Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%}$

$\rm { Loss \: \% = \Bigg( \dfrac{Loss}{C.P} \times 100 \Bigg)\%}$