8th Maths : Chapter 4 : Life Mathematics : Example Problems on Profit, Loss, Discount, Overhead Expenses and GST : Questions with Answers, Solution

**Example
Problems on **

**Profit,
Loss, Discount, Overhead Expenses and GST**

** **

__Example 4.6__

Ranjith bought
a washing machine for ₹16150 and paid ₹1350 for its transportation.

Then, he
sold it for ₹19250. Find his gain or loss percentage.

*Solution:*

Total C.P
of the washing machine

= C.P + Overhead Expenses

= 16150 + 1350 = ₹17500

S.P = ₹19250

Here, S.P
> C.P. Hence, there is a gain.

Gain % = (Gain/C.P ×100) % = { [19250 −17500]/17500 × 100 }% = ( [1750/17500] × 100 ) % =10%

** **

__Example 4.7__

If the selling
price of an LED TV is equal to 5/4 of its cost price, then find the gain / profit
percentage.

*Solution 1:*

*Solution 2:*

Let the C.P
of the LED TV be ₹*x*.

∴ S.P
= 5/4 = *x*

Profit =
S.P – C.P = 5/4 *x *−* x *= *x*/4

Profit %
= (Profit/C.P ×100) %

∴
Profit % = ( *x */ 4 ×100) % = (1/4 ×100)
% = 25%

** **

__Example 4.8__

The cost
price of 16 boxes of strawberries is equal to the selling price of 20 boxes of strawberries.
Find the gain or loss percentage.

*Solution:*

Let the C.P
of one strawberry box be ₹ *x* .

C.P of 20
strawberry boxes = 20 *x* and

S.P of 20
strawberry boxes = C.P of 16 strawberry boxes = 16 *x* (given)

Here, S.P < C.P, hence there is a loss.

Loss = C.P
–S.P = 20 *x* - 16* x *=4 x

Loss % =
( [Loss/ C . P] ×100 ) %

= ([4*x*/20*x*]
×100) %

∴
Loss % = 20 %

If the cost price of *x*
articles = selling price of *y* articles,
then profit % = = ( [*x-y*/*y*] ×100) % . If the answer
is negative, then it is treated as loss. Check and verify this~~ ~~for Example
4.8.

** **

__Example 4.9__

By selling
a bicycle for ₹4275, a shopkeeper loses 5%. For how much should he sell it to have
a profit of 5%?

*Solution:*

S.P of the
bicycle = ₹4275

Loss = 5%

To have a
profit of 5%, he should sell the bicycle for ₹4725.

** **

__Example 4.10__

The price
of a rain coat was slashed from ₹1060 to ₹901 by a shopkeeper in the rainy season
to boost the sales. Find the rate of discount given by him.

*Solution:*

Discount
= Marked Price –Selling Price

= 1060 – 901

= ₹159

∴ Discount % = ( [159/1060] × 100) %

= 15%

** **

**Think**

A shopkeeper marks the price of a marker board 15% above the cost
price and then allows a discount of 15% on the marked price. Does he gain or lose
in the transaction?

**Solution: **

Let cost price of marker board be 100

CP = 100 Marks it 15% above CP

∴ Marked price = MP = ( [15/100]
× CP ) + CP

= ( [15/100] × 100 ) + 100 = 15 + 100 = 115

Discount % = 15%

Discounted price = MP (1 – (*d*%/100)) = 115 (1 – (15/100))
= 115 × (85/100) = 97.75

∴ He sells it 97.75 which is less than his cost price. Therefore
he loses

Loss = 97.75 − 100 = −2.25

** **

__Example 4.11__

Find the
single discount in percentage which is equivalent to two successive discounts of
25% and 20% given on an article.

*Solution:*

Let the marked
price of an article be ₹100.

First discount
of 25% = 100 × (25/100) = ₹25

Price after
first discount = 100 - 25 = ₹75

Second discount
of 20% = 75 × (20/100) = ₹15

Price after
second discount = 75 - 15 = ₹60

Net selling
price = ₹60

Single discount
in percentage equivalent to two given successive discounts = (100–60)% = 40%.

** **

**Note**

• If there are 2 successive discounts of *a* % and *b* % respectively,
then

• Single discount in % equivalent to 3 successive discounts of a
%, b % and c % respectively =

(Use this formula for the Example 4.11 and check the answer).

** **

__Example 4.12__

A water heater
is sold by a trader for ₹10502 including GST at 18%. Find the marked price of the
water heater and GST.

*Solution 1:*

*Solution 2:*

Let the marked
price be ₹ *x* .

Now,* x *+ (18*x*/100)* *= 10502

118*x / *100 = 10502

Marked price,* x *= ₹8900

GST at 18%
= ₹10502 – ₹8900 = ₹1602

(or)

= 8900 × (18/100) = ₹1602

** **

__Example 4.13__

A family
went to a hotel and spent ₹350 for food and paid extra 5% as GST. Calculate the
CGST and SGST.

*Solution:*

Cost of food
= ₹350

Extra 5%
paid as GST is equally shared by the Central and the State Governments at 2.5% each.

CGST = SGST
= 350 ×
(2.5/100) = ₹8.75

Tags : Questions with Answers, Solution | Life Mathematics | Chapter 4 | 8th Maths , 8th Maths : Chapter 4 : Life Mathematics

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