PROFIT AND LOSS II
Type VI : (When two percentage changes are given)
Type VII : (Questions related to marked price)
Type VIII : (Misc. Questions)
Type VI
e.g. A man sold two watches for Rs. 20 each. On one he lost 10% and on another he gained 105.
Find his total loss %.
Sol.
Shortcut
Whether there are two percent changes say A and B then net percent is equal to
AB/100
A+B+
and if the change is increasing or there is a profit then it is taken as positive. If it is decreasing or
there is a loss then it is taken as negative. this short cut is applicable in lot of question of
different types of percentage, profit or loss area etc.
Here A = + 10% (gain)
B = - 10 % (loss)
Net percentage change
= 10 - 10 + 10 X - 10 / 100
=0 - 1 = - 1%
Negative sign shows that there is a loss
Loss= 1%
e.g. A man sold two houses for Rs. 48000 each. On one he lost 20% and another he gained 20%.
Find his total gain or loss in percentage as well as in rupees.
Sol. As discussed earlier this questions a combination of shortcut and concept.
Net percentage change
= - 20 + 20 + -20 * 20 / 100 = 0 - 4
=-4%
Net loss = 4%
Net loss = 4%
Now total SP
96000 which is 96% of CP
965 of CP = Rs. 96000
CP = 96000/96 * 100
= Rs. 100000
Loss = 100000 - 96000
= Rs. 4000
e.g. Two article are sold at 750 Rs. each. One at a profit of 30% another at a loss of 305. Find his
total gain or loss %.
Sol.
By shortcut
Net % change = 30 - 30 + 30 * -30 / 100
= 0 - 9 = -9%
loss is 9%.
Note : This shortcut is applicable if selling price of both the articles as well as profit % on first
and loss % on second are same.
Type VII
e.g.
A tradesman charges 20% above the cost price but allowed a discount of 10% for cash payment,
what is gain percent.
Sol.
Let cost price of item
= Rs. 100
Marked price = Rs. 120
Discount = 120 * 10/100
= Rs. 12
Net SP = 120 - 12 = Rs. 108
Profit % = 8/100 * 100
= 8%
Shortcut
Net % change = 20 - 10 + 20 * -10 / 100
= 10 - 2 = 8%
e.g.
A merchant allows a discount of 105 for cash payment. How much % above the cost price must
he mark his goods, so as to make a profit of 175.
Sol. Net % change = A + B = AB/100
Let mark price is B% above cost price
A = -10%
B = B%
Net % change = 17%
17 = -10 + B + - 10 * B / 100
17 + 10 = B - 10B / 100
27 = 90B / 100
B = 27 * 100 / 90
= 30%
Type VIII
e.g. I bought two horses Rs. 1350. I sold one of them at a loss of 6% and another at a gain of 7
½%. On the whole I neither gained nor lost. What did each horse cost?
Sol. Loss on horse = gain on second
6% 1st cost = 7 ½ % of 2nd cost price
1st horse’s cost price
……………………………… =
2nd horse’s cost price
7½%
……….
6%
= 15 / 2 * 6 = 15 / 12
= 5/4 = 5 : 4
CP of 1st horse = 5/9 * 1350
= Rs. 750
2nd horse = 4/9 * 1350 = Rs. 600
e.g. A sells an article at 10 percent profit. If he had bought it at 10% less and sold it for Rs. 60
less he would have gained 20%. Find the cost price of that article.
Sol. Let CP = Rs. 100
Then SP = Rs. 110
Second CP = Rs. 90
Profit = 20%
Second SP = 90 * 120/100 = Rs. 108
Difference = 110 - 108 = Rs. 2
If difference is 2 Rs. than CP = Rs. 100
= 100/2
= 100/2 * 60 = Rs. 3000