Question

12. Varun sold two almirahs for 2730 each. On one, he lost 9% while on the other he gained 15%. Find his
gain or loss on the whole transaction.
​

Answer 1

$\bold{\large{\underline{\underline{\sf{GiVen :}}}}}$

S.P of an almirah= ₹ 2730

Let the CP of one almirah = Rs x

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

So, according to the question

on loss of 9%

$\sf{ \frac{x - 9x}{100} = 2730}$

$\sf{ \frac{(100x -9x )}{100} = 2730}$

$\sf{ \frac{91x}{100} = 2730}$

91x = 2730 × 100

x= 273000/91

x= 3000

CP =₹ 3000

now, on gain of 15%

x +15x/100 = 2730

(100x +15x) /100= 2730

115x = 2730× 100

x= 273000/115

x= 2,373.91

CP =₹ 2,373.91

Total CP of almirah = 3000 + 2,373.91= 5,373.91

Total CP of almirah =₹ 5,373.91

Total SP of almirah = 2730×2 =₹ 5460

SP > CP

Gain = 5460 - 5,373.91= ₹ 86.09

Gain % = (gain /CP)× 100

= (86.09×100)/ 5,373.91

= 8609/5,373.91

= 860900/5,37391= 1.06%

Gain% = 1.06%

Hence, the gain on the whole transaction is = 1.06%

Answer 2

$\huge{\text{\underline{Question:-}}}$

Varun sold two almirahs for rupees 2730 each on one he lost 9% while on the other He gained 15% find his gain or loss on the whole transaction.

$\huge{\text{\underline{Solution:-}}}$

★ Given:-

• S.P of an almirah = ₹ 2730

★ Assuming:-

Let the CP of one almirah = ₹ x

★ According to question:-

On loss of 9%

x - 9x / 100 = 2730

(100x - 9x ) / 100 = 2730

91x / 100 = 2730

91x = 2730 × 100

x = 273000/91

$\large{\boxed{\text{x = 3000}}}$

Therefore, CP = ₹ 3000

★ Now,

On gain of 15%

x + 15x / 100 = 2730

(100x +15x) /100 = 2730

115x = 2730 × 100

x = 273000 / 115

$\large{\boxed{\text{x = 2,373.91}}}$

Therefore, CP = ₹ 2,373.91

Total CP of almirah = 3000 + 2,373.91

$\large{\boxed{\text{= 5,373.91}}}$

Total CP of almirah = ₹ 5,373.91

Total SP of almirah = 2730 × 2 = ₹ 5460

$\large{\boxed{\text{= Rs.5460}}}$

★ SP > CP

Gain = 5460 - 5,373.91 = ₹ 86.09

$\large{\boxed{\text{= Rs.86.09}}}$

Gain % = (gain / CP) × 100

$\implies$(86.09 × 100)/5,373.91= 8609/5,373.91

$\implies$860900 / 5,37391

$\implies$1.06%

★ Gain% = 1.06%

$\large{\boxed{\text{Gain = 1.06}}}$

Hence, the gain on the whole transaction is = 1.06%.

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