Question 1 1 / -0
If the cost price of 15 tables is equal to the selling price of 20 tables, then the loss percentage in the transaction is
Solution
15 C.P. = 20 S.P.
or
= 0.75 C.P.
Therefore, loss % =
=
= 25
There is 25% loss.
Question 2 1 / -0
Divide Rs. 6270 among A, B and C so that A may receive 3/7 of as much as B and C receive together and B may receive 2/9 of as much as A and C receive together. What amount do A, B and C receive, respectively?
Solution
Let A get Rs. A, B get Rs. B and C get Rs. C.
A + B + C = 6270 …(1)
A =
…(2)
7A = 3B + 3C
Or, 9B = 21A - 9C ...(3)
B =
…(4)
Or, 9B = 2A + 2C ...(5)
From (3) and (5), we get
21A - 9C = 2A + 2C ...(6)
Or, 19A = 11C ...(7)
Or, A = (11/19)C ...(8)
Putting value of A from equation (7) into equation (3), we get
9B = 21(11/19C) - 9C ...(9)
Or, B = (20/57)C ...(10)
Putting values of A and B in terms of C from equations (6) and (10) into equation (1), we get C = 3249 ...(11)
Putting this value of C from equation (11) back into equations (8) and (10), we get A = 1881 and B = 1140.
Thus, A receives Rs. 1881, B receives Rs. 1140 and C receives Rs. 3249.
Thus, answer option (1) is correct.
Question 3 1 / -0
$430 is divided among 45 persons consisting of men, women and children. The sum of shares of men, women and children is in the ratio 12 : 15 : 16, but the individual shares of a man, a woman and a child are in the ratio 6 : 5 : 4. Find the share of each man, woman and child, respectively.
Solution
Share of men = (12/43) × 430 = $ 120
Share of women = (15/43) × 430 = $ 150
Share of children = (16/43) × 430 = $ 160
Ratio of individual share = 6 : 5 : 4
So, individual shares be 6n, 5n and 4n, respectively.
Number of members = 45
n = 2
So, individual shares are $12, $10 and $8, respectively.
Question 4 1 / -0
A total of 500 people voted for a resolution; but after some discussion, the opponents were increased by 100%. The motion was then rejected by a majority, three times as great as that by which it was formerly passed. How many voted for and how many voted against the resolution initially?
Solution
Let the number of opponents be x.
Question 5 1 / -0
An unscrupulous vendor professes to sell guavas at CP, but she uses a weight of 960 gms for a kg weight. The gain % to her is
Solution
Gain % = error % = (100 ´ error)/(true value - error)
= (40/960) ´100 = 100/24 =
Question 6 1 / -0
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A tradesman marks an article at a price which would give him a profit of 20% on the cost price. To the favoured customers, he makes a deduction of 5% from the marked price. What actual profit does he receive from the sale of an article to a favoured customer for which the latter pays him $28.50?
Solution
Let the CP of the article be $x.
MP = x + 20% of x = $1.2x
When a discount is given on this MP,
SP of the article =
× 1.2x = $1.14x
But 1.14x = 28.50
So, x = 25
CP of the article = $25
SP = $28.50
Profit = $3.50
Question 7 1 / -0
A man sells an article at a gain of 10%. If he had bought it at 10% less and sold it for Rs. 132 less, he would have still gained 10%. The cost price of the article is
Solution
SP = 1.1CP
Question 8 1 / -0
The marked price of an article is 40% above the cost price. The discount that may be allowed to make a profit of 12% is
Solution
MP = CP + 40% of CP = 1.4 CP
SP = CP + 12% of CP = 1.12 CP
Percentage discount =
= 20%
Question 9 1 / -0
According to a survey, the population of a city increases by 10% every year for two years and then decreases by 10% every year for two years. If the population 4 years ago was 1,00,000, what will it be after four years?
Solution
Percentage increase (R1) = 10%; n = 2
Percentage decrease (R2) = 10%; n = 2
Population 4 years ago = 1,00,000
Population after 4 years = 1,00,000 (1 +
)
2 (1 -
)
2 = 1,00,000 ×
×
×
×
= 98,010
Question 10 1 / -0
A shopkeeper fixes the marked price of an item 35% above its cost price. What is the percentage of discount allowed to gain 8%?
Solution
MP = 1.35CP
SP = 1.08CP
% discount from the marked price =
× 100
=
× 100 = 20%
Question 11 1 / -0
What will be 70 percent of a number whose 140 percent is 70?
Solution
Let the number be 'x'.
x = 70
⇒ x =
= 50
Now, 70% of 50 =
50 = 35
Question 12 1 / -0
In an examination, 45% of the total examinees passed. If the number of failures is 121, the number of those who passed is
Solution
55% = 121
Therefore, 45% =
.
Question 13 1 / -0
A watch was sold at a loss of 10 percent. If it was sold for $70 more, there would have been a gain of 4 percent. What was the CP of the watch?
Solution
Let the cost price of the watch is $x.
Question 14 1 / -0
A man spends 85% of his income. If he saves $37.50, find the salary.
Solution
Let income be $x
Question 15 1 / -0
In an election between two candidates, Mr. Hero secures 45% of the total votes, but is defeated by Mr. Zero by 300 votes. Find out the total number of votes polled, if it is known that all the votes polled are valid.
Solution
Let the total number of votes polled be x.
Question 16 1 / -0
Calculation shows that an angle is 37 ½, the size obtained by drawing and measurement is 36o ; find the error percent.
Solution
%age error =
= 1.5 ×
= 4.
Question 17 1 / -0
The price of domestic oil is increased by 20%. By how much percent must a family reduce the consumption of oil so that their expenditure may remain the same?
Solution
Here, R= 20
Therefore, the reduction in consumption =
% =
%
Question 18 1 / -0
A man sold an article for $75 and lost something. Had he sold it for $96, his gain would have been double the former loss. The cost price of the article is
Solution
1st case: nd case:
Question 19 1 / -0
Successive discounts of 10% and 20% are equivalent to a single discount of
Solution
Total discount = 10% + 20% - (10 x 20/100)% = 10% + 20% - 2% = 28%
Question 20 1 / -0
A man purchased an article at 3/4 of the list price and sold it at 50% more than the list price. What was his gain percentage?
Solution
CP = 3/4 of list price
SP = 3/2 of list price (half more than list price)
Gain percentage =
× 100 =
× 100 = 100%
Question 21 1 / -0
If 6 men earn 10% of $750 in 10 days, then 8 men will earn 20% of $350 in
Solution
6 men earn 10% of $750 in 10 days.
Amount 1 man earns in 1 day =
8 men earn 20% of $350 in x days.
Amount 1 man earns in 1 day =
So,
=
x =
= 7 days
Question 22 1 / -0
If a merchant estimates his profits as 20% of the selling price, what is his real profit percent?
Solution
Let S.P be Rs. 100
Question 23 1 / -0
In an examination, 65.6% of the candidates took Science and 40.8% took Sanskrit. If 1280 candidates took both the subjects, find the number of candidates that appeared in the examination.
Solution
% age of candidates for Science = 65.6%
% age of candidates for Sanskrit = 40.8%
It shows number of students for both = (65.6 + 40.8 -100) = 6.4%
Now 6.4% of total candidates = 1280
Total candidates =
OR
Let total candidates who appeared in the examination be T
65.6%T - 1280 + 1280 + 40.8%T - 1280 = T
106.4%T - 1280 = T
1.064T - T = 1280
0.064T = 1280
T = 20,000
Question 24 1 / -0
What percent of 7.5 kg is 15 gms?
Solution
1000gm = 1 kg
15 gm = 0.015 kg
Let x% of 7.5 kg is 15 gms
= x
x = 0.20%
Question 25 1 / -0
Gangaram buys 7000 bananas at Rs. 2 each and agrees to pay an additional sum of Rs. 300 for their delivery. He estimated that 10% of the bananas will be spoiled, so he decides a selling price of Rs. 3 each for the remaining. However, during delivery, 20% of the bananas are spoiled. What should be the percent increase in the selling price in order to obtain the same total profit?
Solution
10% decrease means there are 6300 bananas.
Total S.P. = 6300 × Rs. 3 = Rs. 18,900
Actual number of bananas left after 20% decrease = 5600
To keep the profit the same, S.P. of each banana should be Rs.
= Rs. 3.375
Percent increase in S.P. =
= 12.5%
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