Question

Mr. Sinha sold two tape-recorders for 990
each; gaining 10% on one and losing 10% on
the other. Find his total loss or gain, as
percent, on the whole transaction,​

Answer 1

✬ Loss Percent = 1 % ✬

Step-by-step explanation:

Given:

• Selling price of two tape recorders is Rs 990 each.
• On one recorder he gains 10% and on other he losses 10%.

To Find:

• What is his loss of gain percent in whole transaction ?

Solution: In first condition on first recorder

• S.P = Rs 990.
• Gain % = 10%.

As we know to find C.P when S.P and gain % are given we use the formula

★ C.P = (100/100 + gain %) × S.P ★

$\implies{\rm }$ C.P = (100/100 + 10) × 990

$\implies{\rm }$ 100/110 × 990

$\implies{\rm }$ 99000/110

$\implies{\rm }$ 900

So cost price of first recorder is Rs 900.

Now, in second condition on second recorder

• S.P = Rs 990
• Loss % = 10 %

Using formula

★ C.P = (100/100 – loss %) × S.P

$\implies{\rm }$ C.P = (100/100– 10) × 990

$\implies{\rm }$ 100/90 × 990

$\implies{\rm }$ 99000/90

$\implies{\rm }$ 1100

So cost price of second recorder is Rs 1100.

Lets find total s.p & c.p of both recorders.

➯ Total S.P = Rs (990 + 990)

➯ Rs 1980

➯ Total C.P = Rs (900 + 1100)

➯ Rs 2000

On comparing both C.P and S.P

• C.P > S.P (Here is loss)

• Loss = C.P – S.P

• Rs (2000 – 1980) = Rs 20

★ Loss % = (Loss/C.P × 100)

➨ (20/2000 × 100)

➨ 2000/2000

➨ 1 %

Hence his loss percent on whole transaction is 1 %.

Answer 2

Answer:

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✬ Loss Percent = 1 % ✬

Step-by-step explanation:

Given:

Selling price of two tape recorders is Rs 990 each.

On one recorder he gains 10% and on other he losses 10%.

To Find:

What is his loss of gain percent in whole transaction ?

Solution: In first condition on first recorder

S.P = Rs 990.

Gain % = 10%.

As we know to find C.P when S.P and gain % are given we use the formula

★ C.P = (100/100 + gain %) × S.P ★

\implies{\rm }⟹ C.P = (100/100 + 10) × 990

\implies{\rm }⟹ 100/110 × 990

\implies{\rm }⟹ 99000/110

\implies{\rm }⟹ 900

So cost price of first recorder is Rs 900.

Now, in second condition on second recorder

S.P = Rs 990

Loss % = 10 %

Using formula

★ C.P = (100/100 – loss %) × S.P

\implies{\rm }⟹ C.P = (100/100– 10) × 990

\implies{\rm }⟹ 100/90 × 990

\implies{\rm }⟹ 99000/90

\implies{\rm }⟹ 1100

So cost price of second recorder is Rs 1100.

Lets find total s.p & c.p of both recorders.

➯ Total S.P = Rs (990 + 990)

➯ Rs 1980

➯ Total C.P = Rs (900 + 1100)

➯ Rs 2000

On comparing both C.P and S.P

C.P > S.P (Here is loss)

• Loss = C.P – S.P

• Rs (2000 – 1980) = Rs 20

★ Loss % = (Loss/C.P × 100)

➨ (20/2000 × 100)

➨ 2000/2000

➨ 1 %

Hence his loss percent on whole transaction is 1 %.