Question

a man sold two cycles for rupees 3,000 each gain 20% on one and losing 20% on other find the gain or loss percent on the whole transaction
​

Answer 1

Answer:

4% loss

Step-by-step explanation:

Given :

A man sold 2 cycles each at the rate of ₹3,000 , and he gained 20% by selling 1st cycle and lost 20% on 2nd cycle.

To Find :

The overall loss/gain in the transaction.

Solution :

He gained 20% profit on 1st cycle by selling it for ₹3,000

S.P = C.P + $\frac{Profit:\ Percent}{100}$ × C.P

3000 = C.P × $(1 +\frac{20}{100})$

3000 = C.P × $(\frac{100+20}{100})$

3000 = C.P × $(\frac{120}{100})$

3000 × $(\frac{100}{120})$ = C.P

3000 × $(\frac{5}{6})$ = C.P

2500 = C.P

∴ He sold 1st cycle for ₹2,500

__

He lost 20% loss on 2st cycle by selling it for ₹3,000,

S.P = C.P - $\frac{Loss:\ Percent}{100}$ × C.P

3000 = C.P × $(1 -\frac{20}{100})$

3000 = C.P × $(\frac{100-20}{100})$

3000 = C.P × $(\frac{80}{100})$

3000 × $(\frac{100}{80})$ = C.P

3750 = C.P

∴ C.P of 2nd cycle is ₹3,750.

__

Overall S.P = ₹3,000 × 2 = ₹6,000

Overall C.P = ₹2,500 + 3,750 = ₹6,250

Overall profit/loss = $\frac{S.P - C.P}{C.P}$ × 100,(if the result is positive, it is profit(gain),if the result is negative, it's loss)

⇒  $\frac{6000 - 6250}{6250}$ × 100

⇒$\frac{-250}{6250}$ × 100

⇒$\frac{-1}{25}$ × 100

⇒$\frac{-1X100 }{25}$ = $\frac{-100 }{25}$ = -4%

∴ He lost 4% on the whole transaction.

Answer 2

Answer:

Answer:

4% loss

Step-by-step explanation:

Given :

A man sold 2 cycles each at the rate of ₹3,000 , and he gained 20% by selling 1st cycle and lost 20% on 2nd cycle.

To Find :

The overall loss/gain in the transaction.

Solution :

He gained 20% profit on 1st cycle by selling it for ₹3,000

S.P = C.P + \frac{Profit:\ Percent}{100}

100

Profit: Percent

× C.P

3000 = C.P × (1 +\frac{20}{100})(1+

100

20

)

3000 = C.P × (\frac{100+20}{100})(

100

100+20

)

3000 = C.P × (\frac{120}{100})(

100

120

)

3000 × (\frac{100}{120})(

120

100

) = C.P

3000 × (\frac{5}{6})(

6

5

) = C.P

2500 = C.P

∴ He sold 1st cycle for ₹2,500

__

He lost 20% loss on 2st cycle by selling it for ₹3,000,

S.P = C.P - \frac{Loss:\ Percent}{100}

100

Loss: Percent

× C.P

3000 = C.P × (1 -\frac{20}{100})(1−

100

20

)

3000 = C.P × (\frac{100-20}{100})(

100

100−20

)

3000 = C.P × (\frac{80}{100})(

100

80

)

3000 × (\frac{100}{80})(

80

100

) = C.P

3750 = C.P

∴ C.P of 2nd cycle is ₹3,750.

__

Overall S.P = ₹3,000 × 2 = ₹6,000

Overall C.P = ₹2,500 + 3,750 = ₹6,250

Overall profit/loss = \frac{S.P - C.P}{C.P}

C.P

S.P−C.P

× 100,(if the result is positive, it is profit(gain),if the result is negative, it's loss)

⇒ \frac{6000 - 6250}{6250}

6250

6000−6250

× 100

⇒\frac{-250}{6250}

6250

−250

× 100

⇒\frac{-1}{25}

25

−1

× 100

⇒\frac{-1X100 }{25}

25

−1X100

= \frac{-100 }{25}

25

−100

= -4%

∴ He lost 4% on the whole transaction.