1. A shopkeeper mixes two varieties of Tea, one costing Rs. 40/kg and another Rs. 50/kg in the ratio 3:2. if he sells the mixed variety of Tea at Rs. 48/kg, his gain or loss percent is
Options:
A. 25%
B. 30%
C. 20%
D. 10%
Solution:
Average CP of Mixed Tea when Mixed in Ratio 3:2
$= \frac{40 \times 3 + 50 \times 2}{3 + 2} = \frac{220}{5} = Rs.44$
When SP = Rs. 48/kg
Therefore, CP of 1 Kg
$= \frac{4}{44} \times 100 = 9.90 \approx{10} %$
Correct option: D
2.A bar tender served a jar full of vodka containing 50% alcohol to a customer. After few minutes, the customer asked the bar tender to replace the vodka by another drink containing 19% alcohol and now the percentage of alcohol was found to be 25%. Find out the quantity of vodka replaced?
Options:
A.$ \frac{25}{31}$
B.$ \frac{20}{31}$
C.$ \frac{1}{2}$
D. $\frac{31}{20}$
Solution:
By the rule of alligation, we have:
Ratio of 1st and 2nd quantities = 6: 25
By the rule of ratio, if x:y is the ratio, to get the quantity of x, the formula is $\frac{x}{x+y}$,and to get the quantity of y, the formula is $\frac{y}{x+y}$
Therefore, required quantity replaced = $\frac{25}{25 + 6} = \frac{25}{31}$
Correct option: A
3. One type of liquid contains 25% of milk, the other contains 30% of milk. A container is filled with 6 parts of the first liquid and 4 parts of the second liquid. The percentage of milk in the mixture is:
Options:
A. 27%
B. 32%
C. 19%
D. 30%
Solution:
Let the quantity of a container is 10
So, milk from the first liquid $ 6 \times \frac{25}{100} = 1.5$
And, milk from 2nd liquid $ 4 \times \frac{30}{100} = 1.2$
Total milk = 1.5 + 1.2 = 2.7
In terms of percentage = $\frac{2.7}{10} ×100 = 27%$
Correct Option: A
1.If 40% of a number is equal to ${\frac{2}{3}}^{rd}$ of another number, what is the ratio of first number to the second number?
Options:
A. 1: 2
B. 2: 3
C. 3: 5
D. 5: 3
Solution:
Let the two numbers be x and y
40% of x = $\frac{2}{3}y$
Then, $\frac{40x}{100} = \frac{2}{3}$
$\frac{2}{5} = \frac{2}{3}$
$\frac{x}{y} = \frac{2}{3} × \frac{5}{2} = \frac{5}{3}$
Therefore the ratio = 5: 3
Correct option: D
2. In a box of 10 cakes ,5 cakes have Choco chip sprinkle on them. Find out how many percent of the cakes in the box has Choco chip sprinkle?
Options:
A. 50%
B. 40%
C. 25%
D. 20%
Solution:
$\frac{5}{10} = \frac{x}{100}$
2x = 100
x = \frac{100}{2}$
x = 50%
Correct option: A
3.Two numbers are respectively 40% and 80% more than a third number. The ratio of the two numbers is:
Options:
A. 6: 5
B. 7: 9
C. 2: 5
D. 1: 2
Solution:
Let the third number x
First number = 40 % more than $x = \frac{140}{100}x$ =$ \frac{7}{5}x$
Second number = 80% more than x =$ \frac{180}{100}x$ =$ \frac{9}{5}x$
Therefore their ratio = $\frac{7}{5}x: \frac{9}{5} x = 7: 9$
Correct Option: B
1.Radhika spends 40% of her salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If her savings at the end of a month are Rs 1500, then what is her monthly salary?
Options:
A. Rs. 5500
B. Rs. 8500
C. Rs. 7500
D. Rs. 6000
Solution:
Let Radha's monthly salary be Rs x.
Then, from the given data we can write
40% of x+20% of x+10% of x+10% of x+ Rs 1500=x
⇒$ \frac{40}{100} \times x + \frac{20}{100} \times x + \frac{10}{100} \times x + \frac{10}{100} \times x + Rs 1500 = x$
$\implies \frac{80x}{100} + 1500 = x$
$\implies x - \frac{4x}{5} = Rs. 1500$
$\frac{x}{5} = Rs. 1500$
$\implies x = 1500 \times 5 = Rs 7500 $
Correct option: C
2. A man spends 60% of his income. If his income increases by 15% and his expenditure increases by 15%. Find the percentage change in his saving.
Options:
A. 15%
B. 18%
C. 25%
D. 45%
Solution:
Income - Expenditure = Saving
Let the income be 100x
A man spends 60% of his income
Expenditure = 60x
⇒ 100x - 60x = 40x
Savings = 40x
Income increases by 15%
⇒ 100x + 15x = 115x
Expenditure increases by 15%
⇒ 15% = 3/20
Increase of 15% = 23/20
⇒ 60x × 23/20
⇒ 69x
New savings = 115x - 69x = 46x
Change in savings
⇒ 46x - 40x = 6x
Percentage increase in saving = (6x/40x) × 100 = 15%
∴ Percentage increase in saving is 15%
Trick :
When income and expenditure are increased/decreased respectively by the same percentage of the amount i.e. x%, then the percentage change in (income - expenditure) i.e. saving would also be x%.
So, here percentage change in saving = 15%
Correct option: A
3. Suresh salary was decreased by 30% and subsequently increased by 40%. How much percent does she loose?
Options:
A. 2%
B. 7%
C. 5%
D. 4%
Solution:
cording to the formula, Suresh loose percentage =$ -30 + 40 + \frac{(-30)(+40)}{100} = 10 - 2 = -2 %$
It means He lost Total 2% of his salary.
Correct Option: A
1.The population of Udaipur increased from 100000 to 250000 in 10 years. The average percent increase of population per year is:
Options:
A. 5%
B. 15%
C. 25%
D. 40%
Solution:
Increase of population in 10 years = 250000 – 100000 = 150000
Increase % = $\frac{150000}{100000 }× 100 = 150%$
Monthly Expenditure =
Required average $= \frac{150}{10}% = 15%$
Correct option: B
2.Population of a town increases by 10% in 1st year. Again, it increased by 20% in next year. Calculate the equivalent net % increase?
Options:
A. 35%
B. 25%
C. 23%
D. 32%
Solution:
Final Population= Initial Population $\frac{150}{10}$
increase in first Year × increase in second Year = Initial Population × $(1+ \frac{10}{100})(1+ \frac{20}{100})$
Final Population= Initial Population × 1.1 × 1.2
Final Population= Initial Population × 1.32
So, here net Multiplying Factor =1.32 = which means 32% increase
Correct option: D
3.The current population of a village is 12000. If it increases at the rate of 5% p.a. then at the end of 2 years, it will be:
Options:
A. 13230
B. 13320
C. 13200
D. 13323
Solution:
Current population of thevillage = 12000
Increase rate = R = 5%
We know that,
The population after 2 years = P *(1 + R/100)n = 12000 * (1 + 5/100)²
$= 12000 ×(\frac{105}{100})^2$
$= 12000 × \frac{105}{100} × \frac{105}{100}$
Correct Option: A
1.A fruit seller had some oranges. He sells 40% oranges and still has 540 oranges. Find out the total oranges he had?
Options:
A. 1000
B. 420
C. 460
D. 900
Solution:
Let the total oranges be x
So, 1(00- 40)% of x = 540
$\frac{60}{100}$ of x = 540
= $540 × \frac{100}{60}$ = 900
Correct option: D
2.Rakesh brought 100 apples at the rate of Rs. 250. He sold them at the rate of Rs. 50 per dozen. Find the percentage of profit or loss?
Options:
A. 66.4% gain
B. 66.4% loss
C. 60.4% gain
D. 66.2% gain
Solution:
CP of one apple = $ \frac{250}{100}$ = Rs. 2.50
SP of one apple = $\frac{50}{12} = Rs 4.16 $
It is clear, that S.P. > C. P, therefore, there is gain.
Gain % = $\frac{SP – CP}{CP}× 100$
Gain % = 66.4%
Correct option: A
3. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A. 8%
B. 5%
C. 10%
D. 12%
Solution:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain $ = \frac{80}{1600} \times 100$
Correct Option: B
1.Ram was multiplying a number. By mistake he multiplied $\frac{2}{5}$ instead of $\frac{5}{2}$. What is the percentage error in the calculation?
Options:
A. 84%
B. 89%
C. 78%
D. 94%
Solution:
Let the number be x
Error = $\frac{5}{2} – \frac{2}{5}x = \frac{21x}{10}$
Error % = $\frac{21x}{10}x × \frac{5}{2x}× 100 = 84%$
Correct option: A
2.If P = x% of y and Q = y% of x, then which of the following is true?
Options:
A. P is smaller than Q
B. P is greater than Q
C. P is equal to Q
D. Cannot be determined
Solution:
P = x% of y = $\frac{x}{100}$ x y
Q = y% of $x = \frac{y}{100}y × x$
$\frac{x}{100}x × y = \frac{y}{100}$
$\frac{xy}{100} xy= \frac{yx}{100}$
Therefore, P = Q
Correct option: C
3. What percentage of numbers from 1 to 50 have 5 in the unit’s digit?
Options:
A. 10%
B. 20%
C. 30%
D. 25%
Solution:
Clearly, the numbers which have 0 or 5 in the unit’s digit from 1 to 50 are 5, 15, 25, 35 and 45
Total numbers are = 5
Required percentage $ = \frac{5}{50}× 100 = 10\%$
Correct Option: A