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Start from the root of 169 then second root will reduce to 11, third root will reduce to 7, fourth root will reduce to 8, and finally, it reduce to value 4.
Put a = 5 and b = 3 in given equation
hence it will be 5^{3} = 125
The first and last terms of an arithmetic progression are 23 and 42. What is the sum of the series if it has 14 terms?
In an arithmetic progression with first term, a = 23, last term, l = 42
Number of terms = n = 14
7 × 19 = 133
=> Ans  (B)
Product of: 6ab, 3b and 4a
= (6 × 3 × 4) × (ab × b × a)
= 72a^{2}b^{2}
=> Ans  (A)
Expression: 2714/5074
HCF of 2714 and 5074 = 118
Dividing numerator and denominator by 118
= 23/43
=> Ans  (C)
The average of five numbers is 56.4. The average of the first and the second number is 53. The average of the fourth and the fifth number is 56. What is the third number?
Average of 5 numbers is given as 56.4
Total of 5 numbers = Average x Number of Elements
Total of 5 numbers = 56.4 x 5 = 282
Average of 1st and 2nd number is 53
Total of 1st and 2nd number = 53 x 2 = 106
Average of 4th and 5th number is 56
total of 4th and 5th number = 56 x 2 = 112
1st + 2nd + 3rd + 4th + 5th = 282
106 + 3rd + 112 = 282
3rd = 64
hence option A is correct
The cost price of an article is 64% of the marked price. The gain percentage after allowing a discount of 12% on the market price is
Let's say marked price = 100
Then cost price = 64
and selling price = 88
discount = 24
The number of seats in an auditorium is increased by 25%. The price of a ticket is also increased by 12%. Then the increase in revenue collection will be
Let's assume no. of seats were 100 and price of a ticket was 100 hence total revenue is 10000.
Now acc. to question after increment no. of seats will be 125 and price of a ticket will be 112. Hence total revenue will be 125 * 112 = 14000.
Increment in revenue = 4000
% increase in revenue = 40%
In a factory 60% of the workers are above 30 years and of these 75% are males and the rest are females. If there are 1350 male workers above 30 years, the total number of workers in the factory
Let's say total number of workers are xx.
Hence above 30 years workers will be 60x/100
And male workers will be
So x will be = 3000.
In a partnership business, A invests 1/6th of the capital for 1/6 of the total time, B invests 1/4 of the capital for 1/4 of the total time and C, the rest of the capital for the whole time. Out of a profit of 19,400, B's share is:
Let the total capital be Rs z and total time be y
hence ratio of profit divison for A, B, C will be
A : B : C = 4 : 9 : 84
hence profit for B = 9/97 x 19400 = 1800
The average marks obtained by a student in 6 subjects is 88. On subsequent verification it was found that the marks obtained by him in a subject was wrongly copied as 86 instead of 68. The correct average of the marks obtained by him is
Number of subjects = 6
wrong average = 88
sum of marks calculated wrongly in all subjects = 88 x 6 = 528
Correct Marks = 528  86 + 68 = 510
Correct Average of marks = 510/6 = 85
A sum of Rs 76 is divided among A, B and C in such a way that A gets 7 more than that what B gets and B gets 6 more than what C gets. The ratio of their shares is
Let the amount with C be Rs y
so, amount with B = y +6
and amount with A = y + 13
and it is given that total amount is 76, So
y + y + 6 + y + 13 = 76
y= 19
Hence A : B : C = 32 : 25 : 19
A reduction of 20% in the price of sugar enables me to purchase 5 kg more for Rs. 100. Find the price of sugar per kg before reduction of price.
cost of 5 kg. rice = 100 rs.
cost of 1 kg. rice = 20 rs.
Before discount cost price will be =
Directions: The pie chart given below show the spending of a family on various heads during a month. Study the graph and answer the questions.
If the total income of the family is Rs. 25,000, then the amount spent on Rent and Food together is
Total share percentage on food and rent = 45 + 14 = 59%
Hence price will be = 25000 × 59100 = 14750
An article which is marked at Rs. 975 is sold for Rs.897. The discount percent is
Marked price(M) of article = Rs 975
Selling Price (S) of article = Rs 897
= 8%
Slope of the line AB is 4/3. Coordinates of points A and B are (x, 5) and (5, 3) respectively. What is the value of x?
→ 24 = 20 + 4x
→ x = 1
so the answer is option D.
What is the reflection of the point (2, 5) in the line x = 1?
Reflection of point (x, y) in line x = a is (x + 2a, y)
Now, Reflection of point (2, 5) in line x = 1
= [2 + 2(1), 5] = (0, 5)
=> Ans  (B)
What is the slope of the line parallel to the line passing through the points (4, 2) and (3, 5)?
Slope of line passing through points (4, 2) and (3, 5)
Slope of two parallel lines is always equal.
=> Slope of the line parallel to the line having slope 1 = 1
=> Ans  (D)
What is the reflection of the point (3, 1) in the line x = 2?
Reflection of point (x, y) in line x = a is (x + 2a, y)
Now, Reflection of point (3, 1) in line x = 2
= [3 + 2(2), 1] = (1, 1)
=> Ans  (A)
Point A divides segment BC in the ratio 4 : 1. Coordinates of B are (6 , 1) and C are (7/2, 6). What are the coordinates of point A?
(x, y) = (4, 5)
So the answer is option B.
Directions: The following graph shows the production of cotton bales of 100 kg each in lakhs by different states A, B, C, D and E over the years. Study the graph and answer the following Questions.
How many kg of cotton was produced by State C during the given period?
Production of C in year 20032004 = 6 per 100 kg in lakh
in year 200405 = 11 per 100 kg in lakh
in year 200506 = 15 per 100 kg in lakh
Total will be 32 per 100 kg in lakh or 320000000 kg
Study the following bar diagram carefully and answer the following questions.
The number of the production of electronic items (TVs and LCDs) in a factory during the period from 2009 to 2013.
The total number of products of electronic items is maximum in the year
Total no. of electronic items in:
2009 = 6000 + 7000 = 13000
2010 = 9000 + 9400 = 18400
2011 = 13000 + 9000 = 22000 [MAX]
2012 = 11000 + 10000 = 21000
2013 = 8000 + 12000 = 20000
=> Total production is maximum in 2011
In the following questions, the graph shows the demand and production of different companies. Study the graph and answer the questions.
The production of company A is approximately what percent of the demand of company C?
Production of Company A = 1400 lakh tonnes
Demand of company C = 2600 lakh tonnes
Production of company A as a percentage of demand of company C = 1450/2600 = 55% (Approx)
Option D is the right answer.
In the following questions, the graph shows the demand and production of different companies. Study the graph and answer the questions.
What is the difference between the average demand and the average production of the companies (in lakh tonnes)? [Approximately]
Total demand = 2100 + 3150 + 2600 + 5000 + 2800 + 3300 = 18950
Total supply = 1450 + 3650 + 3100 + 4200 + 3700 + 4500 = 20600
Difference in total demand and supply = 1650
Average difference = 1650/6 = 275
Hence, option C is the right answer.
The graph shows the result of 10th class students of a school for 4 years. Study the graph and answer the questions:
The ratio of students who scored second class to the total students appeared in the year 2000 is
In 2000, no. of students who passed with:
1st class = 90
2nd class = 50
3rd class = 20
Total students = 90 + 50 + 20 = 160
=> Required ratio = 50/160 = 5 : 16
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