Question

Manoj bought a mixer for ₹ 1600 and sold it to Rajan at a profit of 5%. Rajan sold the same Sandeep at a profit of 10% How much did Sandeep pay for the mes?​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Manoj brought mixer for 1600Rs.

• Manoj sold mixer to Rajan at 5% profit.

• Rajan sold mixer to Sandeep at 10% profit.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Price at which Sandeep bought the mixer.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Manoj sells mixer to Rajan at 5% profit.

→ Buying price (Rajan) = 1600 + (5% of 1600)

ㅤㅤㅤㅤㅤ= 1600 + (5/100)(1600)

ㅤㅤㅤㅤㅤ= 1600 + 80

ㅤㅤㅤㅤㅤ= 1680 Rs

Rajan bought mixer at 1680Rs.

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→ Rajan sells Sandeep at 10% profit.

Buying price (Sandeep) = 1680 + (10% of 1680)

ㅤㅤㅤㅤㅤ= 1680 + (10/100)(1680)

ㅤㅤㅤㅤㅤ= 1680+168

ㅤㅤㅤㅤㅤ= 1848Rs

Hence , Sandeep bought mixer at 1848Rs.

Answer 2

Correct Question:

• Manoj bought a mixer for ₹ 1600 and sold it to Rajan at a profit of 5%. Rajan sold the same Sandeep at a profit of 10% How much did Sandeep pay for the mixer?

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Formula used:

• $\bf\: S.P. = \bigg [\dfrac{C.P \times (100 \: + \: gain\%)}{100} \bigg]$

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Required Solution:

Cost price for Manoj = ₹1600

⠀⠀⠀⠀⠀⠀⠀⠀He gain = 5%

${ \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\sf\: S.P. = \bigg [\dfrac{C.P \times (100 \: + \: gain\%)}{100} \bigg]}} \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \bigg[\dfrac{1600 \times (100 \: + \: 5)}{100} \bigg] \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \bigg[\dfrac{16 \cancel{00} \times (105)}{1 \cancel{00}} \bigg] \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \: 16 \times 105 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \: { \underline{ \boxed{ \bf{ \bigstar{ \pink{1680}}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Now, cost price for Rajan = ₹1680

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀He Gain⠀= 10%

${ \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\sf\: S.P. \: for \: Rajan= \bigg [\dfrac{C.P \times (100 \: + \: gain\%)}{100} \bigg]}} \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \bigg[\dfrac{1680 \times (100 \: + \: 10)}{100} \bigg] \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \bigg[\dfrac{168 \cancel{0} \times 11 \cancel{0}}{1 \cancel{00}} \bigg] \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \: 168 \times 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: S.P \: = ₹ \: { \underline{ \boxed{ \bf{ \bigstar{ \pink{1848}}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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• Hence, Sandeep got it ₹1848