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If the numerator of a fraction is increased by 20% and the denominator is increased by 25% , the fraction obtained is `(3)/(5)` . What was the original fraction ?
A. `(5)/(7)`
B. `(4)/(7)`
C. `(3)/(8)`
D. None of these
Correct Answer - D(d) Let fraction be `(x)/(y)` `:.` According to the question , `( x xx 120%)/( y xx 1250%)=(3)/(5)` `implies (x)/(y)=(3)/(5)xx(125)/(120)=(5)/(8)`
Correct Answer – D
See less(d) Let fraction be `(x)/(y)`
`:.` According to the question , `( x xx 120%)/( y xx 1250%)=(3)/(5)`
`implies (x)/(y)=(3)/(5)xx(125)/(120)=(5)/(8)`
The value of a machine depreciates at the rate of 25% each year. If the difference between its value at the end of the second year and the third year is Rs.24,000, then what is the value (in Rs.) of the machine at the end of the first year?
1. 1,28,000
2. 1,00,000
3. 1,35,000
4. 1,12,000
Correct Answer - Option 1 : 1,28,000Given:The value of a machine depreciates at the rate of 25% each year.Concept Used:Price after depreciation = Original price × (100 - depreciation %)/100Calculation:Let value of the machine at the end of first year be Rs.aThe value of the machine at the end of secRead more
Correct Answer – Option 1 : 1,28,000
Given:
The value of a machine depreciates at the rate of 25% each year.
Concept Used:
Price after depreciation = Original price × (100 – depreciation %)/100
Calculation:
Let value of the machine at the end of first year be Rs.a
The value of the machine at the end of second year = a × 75/100
The value of the machine at the end of third year = a × 75/100 × 75/100
Accordingly,
a × 75/100 – a × 75/100 × 75/100 = 24000
⇒ a = 128000
∴ The value of machine at the end of first year is Rs.128000.
See lessA person’s salary has increased from Rs. 7,000 to Rs. 12,000. What is the percentage increase in his salary?
1. \(61 \frac{1}{7}\)%
2. \(76 \frac{4}{7}\)%
3. \(69 \frac{1}{7}\)%
4. \(71 \frac{3}{7}\)%
Correct Answer - Option 4 : \(71 \frac{3}{7}\)%Given:Initial salary = Rs. 7000Increased salary = Rs. 12,000Calculation: Increase in salary = Rs. 12000 – Rs. 7000 = Rs. 5000Increase % in salary = (5000/7000) × 100 \(\Rightarrow 71\frac{3}{7}\)%∴ The percentage increase in the salary is \(71\frac{3}{7Read more
Correct Answer – Option 4 : \(71 \frac{3}{7}\)%
Given:
Initial salary = Rs. 7000
Increased salary = Rs. 12,000
Calculation:
Increase in salary = Rs. 12000 – Rs. 7000 = Rs. 5000
Increase % in salary = (5000/7000) × 100
\(\Rightarrow 71\frac{3}{7}\)%
∴ The percentage increase in the salary is \(71\frac{3}{7}\)%
See lessIn an exam, total marks gained by four students were 720.5. A got 10% less than B, B got 30% more than C and C got 25% less than D. If A got 175.5 marks, how much marks did D get in the examination?
1. 200
2. 150
3. 175
4. 250
Correct Answer - Option 1 : 200Given:Total marks = 720.5A got 10% less than B, B got 30% more than C and C got 25% less than D.A got marks = 175.5Calculation:Marks obtained by given person in terms of another person = Marks obtained by another person +/- markspercentage by which another person obtaiRead more
Correct Answer – Option 1 : 200
Given:
Total marks = 720.5
A got 10% less than B, B got 30% more than C and C got 25% less than D.
A got marks = 175.5
Calculation:
Marks obtained by given person in terms of another person = Marks obtained by another person +/- markspercentage by which another person obtains more/less marks than the given person
Calculation:
Let the marks obtained by D be x.
C got 25% less than D.
C = x – 25% of x
⇒ 75% of x = 0.75x
B got 30% more than C.
B = 0.75x + 30%of 0.75x
⇒ 0.75x + 0.225x
⇒ 0.975x
A got 10% less than B.
A = 0.975x – 10% of 0.975x
⇒ 0.975x – 0.10 × 0.975x
⇒ 0.8775x
A got marks = 175.5
⇒ 0.8775x = 175.5
⇒ x = 175.5/0.8775
⇒ x = 200 marks
∴ D obtained 200 marks.
See lessIf 20% of P = 30% of Q = 1/6 of R, then P: Q : R is equal to:
1. 1 : 2 : 4
2. 5 : 10 : 6
3. 15 : 10 : 18
4. 2 : 5 : 8
Correct Answer - Option 3 : 15 : 10 : 18Given: 20% of P = 30% of Q = 1/6 of RCalculation:Let 20/100 × P = 30/100 × Q = 1/6 × R = k⇒ P/5 = 3Q/10 = R/6 = k⇒ P = 5k⇒ Q = 10k/3⇒ R = 6k∴ P : Q : R = 5k : 10k/3 : 6k⇒ 15k : 10k : 18k = 15 :10 : 18∴ The correct answer is 15 : 10 : 18
Correct Answer – Option 3 : 15 : 10 : 18
Given:
20% of P = 30% of Q = 1/6 of R
Calculation:
Let 20/100 × P = 30/100 × Q = 1/6 × R = k
⇒ P/5 = 3Q/10 = R/6 = k
⇒ P = 5k
⇒ Q = 10k/3
⇒ R = 6k
∴ P : Q : R = 5k : 10k/3 : 6k
⇒ 15k : 10k : 18k = 15 :10 : 18
∴ The correct answer is 15 : 10 : 18
See lessA student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination?
1. 100
2. 120
3. 150
4. 300
Correct Answer - Option 3 : 150Given:A student has to get 40% marks to pass an examinationCalculation:Let be assume the total marks of the examination is X⇒ X × (40/100) = 30 + 30⇒ X = 150∴ The required result will be 150.
Correct Answer – Option 3 : 150
Given:
A student has to get 40% marks to pass an examination
Calculation:
Let be assume the total marks of the examination is X
⇒ X × (40/100) = 30 + 30
⇒ X = 150
∴ The required result will be 150.
See lessThe average pass percentage of girls in class XII examination in a school is 80 and that of boys is 75. The average pass percentage in class XII of that school is 76.5. Find the percentage of the number of boys in class XII of the school.
1. 72%
2. 60%
3. 70%
4. 65%
Correct Answer - Option 3 : 70%Given:Average pass percentage of girls in class XII examination = 80%Average pass percentage of boys in class XII examination = 75%Average pass percentage in class XII of that school = 76.5%Calculation:Let the number of girls and boys be x and y respectivelyAccording tRead more
Correct Answer – Option 3 : 70%
Given:
Average pass percentage of girls in class XII examination = 80%
Average pass percentage of boys in class XII examination = 75%
Average pass percentage in class XII of that school = 76.5%
Calculation:
Let the number of girls and boys be x and y respectively
According to the question,
80x + 75y = 76.5 × (x + y)
⇒ 80x + 75y = 76.5x + 76.5y
⇒ 3.5x = 1.5y
⇒ 7x = 3y
⇒ x : y = 3 : 7
Percentage of number of boys in school = (7/10) × 100%
⇒ 70%
∴ The percentage of the number of boys in class XII of the school is 70%
See lessTwo students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
1. 52, 43
2. 42, 31
3. 42, 32
4. 42, 33
Correct Answer - Option 4 : 42, 33Given:One student score 9 marks more than the other student.The same student gets marks 56% of the sum of their marks.Calculation:Let the marks of one student be x.Let the marks of other student be (x + 9).The sum of their marks = x + x + 9 = 2x + 9According to theRead more
Correct Answer – Option 4 : 42, 33
Given:
One student score 9 marks more than the other student.
The same student gets marks 56% of the sum of their marks.
Calculation:
Let the marks of one student be x.
Let the marks of other student be (x + 9).
The sum of their marks = x + x + 9 = 2x + 9
According to the question;
⇒ (x + 9) = 56/100 × (2x + 9)
⇒ (x + 9) = 14/25 × (2x + 9)
⇒ 25x + 225 = 28x + 126
⇒ 3x = 99
⇒ x = 33
The marks of the one student = 33
The marks of the other student = 33 + 9 = 42
∴ The marks of the both students is 33, 42.
See lessIn an election, a candidate secures 40% of the votes but is defeated by the only other candidate by a majority of 2980 votes. Find the total number of votes recorded.
1. 15300
2. 15800
3. 14700
4. 14900
Correct Answer - Option 4 : 14900Given:In an election, a candidate secures 40% of the votes but is defeated by the only other candidate by a majority of 2980 votes.Calculations:Let the total votes polled be x other candidate got 60% of the votes.According to the question,(60 – 40)% of x = 2980⇒ (20/Read more
Correct Answer – Option 4 : 14900
Given:
In an election, a candidate secures 40% of the votes but is defeated by the only other candidate by a majority of 2980 votes.
Calculations:
Let the total votes polled be x
other candidate got 60% of the votes.
According to the question,
(60 – 40)% of x = 2980
⇒ (20/100) × x = 2980
⇒ x = 2980 × 5 = 14900
∴ the total number of votes recorded is 14900.
See lessA radioactive atom decays 10% of radioactivity in every 40 minutes. If the current radioactivity of the atom is 35 curie, find what will be its reactivity after 2 hours?
1. 22.9 curie
2. 23.9 curie
3. 19.9 curie
4. 20.9 curie
Correct Answer - Option 1 : 22.9 curieGiven:Radioactivity of the atom = 35 curieDecay rate = 10% of present reactivityConcept:Since, the candle loses its length after 40 minutes seconds, so it will lose its reactivity 3 times in 2 hours. Use successive decrease percentage formula to calculate the reRead more
Correct Answer – Option 1 : 22.9 curie
Given:
Radioactivity of the atom = 35 curie
Decay rate = 10% of present reactivity
Concept:
Since, the candle loses its length after 40 minutes seconds, so it will lose its reactivity 3 times in 2 hours. Use successive decrease percentage formula to calculate the reactivity after 2 hours.
Calculation:
% decrease in reactivity after 40 minutes;
= -10 -10 + (100/100)
= -19%
% decrease after 80 seconds;
= – 19 – 10 + (19 × 10)/100
= -29 + 1.9
= 27.1%
% decrease after 120 seconds;
= – 27.1 – 10 + (27.1 × 10)/100
= – 37.1 + 2.71
= 34.39%
∴ % decrease in radioactivity after 120 minutes = 34.39%
Radioactivity after 120 minutes = 100% – 34.39% = 65.61% of 35 curie
= 22.9 curie
See less