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x^{2}  xy = y .....(1)
y^{2}  xy = 3 .....(2)
Subtracting equation (2) from equation (1) we
Putting the value of x  y in equation (1) we get
Putting value of x in equation (2) we get,
putting value of y in equation (2) we get
y^{2}  xy = 3
⇒ 9  3x = 3
⇒3x  3 9 =  12
⇒ x = 4
So, (x, y) = (4, 3) or (4, 3)
An expression, which when divided by(x+1) gives (x^{2}x+1) as quotient and 3 as remainder, is equal to
A square is inscribed in a circle of radius 10 units. The area of the circle not included in the square......(use π = 3.14)
Let the side of square be x unit.
sider the right triangle ABD
have x^{2} + x^{2} = (10 + 10)^{2}
⇒ 2x^{2} = 400
x^{2} = 200
Area of square = 200 sq units
One of circle = πr^{2} = 22/7 x (10)^{2} = 314 sq units
One of shaded region not included in square
= 314 sq unit  200 sq unit
= 114 sq unit.
Size of a tile is 9 inches by 9 inches. The number of tiles needed to cover a floor of 12 feet by 12 feet is
Length of floor = 12 feet
Breath of floor = 12 feet
So Area of floor = 12 x 12 = 144 feet
Area of tile = 9/12 x 9/12 = 9/16 feet
So the number of tile = = 256 tiles
In a certain yr, the average monthly income of a person is Rs 3400 and that for the first 8 months is Rs 3160 and for the last 5 months is Rs 4120. The income in the eight month of the year is
x_{1} + x_{2} + ..... + x_{12} = 3400 x 12 .....(i)
x_{1} + ..... + x_{8} = 3160 x 8 .....(ii)
x_{8} + ..... + x_{12} = 4120 x 5 .....(iii)
from (i) and (ii)
x_{9} + ..... + x_{12} = 40800  25280 = 15520 .....(iv)
from (iii) and (iv) the income in the eight month of the year
x_{8} = 20600  15520 = Rs. 5080
if the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0
A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pays Rs 680.40 as the price including the sales tax, what is the marked price of the item?
Two numbers,both greater than 29, have HCF 29 and LCM 4147. The sum of the numbers is
Product of numbers = 29 × 4147
Let the numbers be 29a and 29b
Then, 29a × 29b = (24 × 4147)
⇒ ab = 143
Now, coprimes with product 143 are (1, 143) and (11, 13)
So,the numbers are (29 × 1, 29 × 143) and (29 × 11, 29 × 13)
Since both numbers are greater than 29, the suitable pair is (29 × 11, 29 × 13)
i.e., (319, 377)
∴ Required sum = (319 + 377) = 696
AB and CD are two diameters of circles which are perpendicular to each other. The length of the chord BD is
A light house is 60 metres high with its base being at the sea level.If the angle of depression of a boat in the sea from the top of the light house is 15º,then the distance of the boat from the foot of the light house is equal to
How many digits in all are required to write numbers from 1 to 50?
1 to 9 = 9 (1 digit number)
10 to 50 = 41(2 digit number) = 41 x 2 = 82
total digits = 82 + 9 = 91
Suresh's monthly income is 30% more than that of Vinod. Vinod's monthly income is 20% less than that of Vinay.If the difference between the monthly incomes of Suresh and Vinay is Rs 800.What is the monthly income of Vinod?
Suresh = Vinod + 30% of Vinod
= 1.3 Vinod
Vinod = Vinay  20% of Vinay
= 80% of Vinay
= 0.8 Vinay
∴ Suresh = 1.3 x 0.8 Vinay
= 1.04 Vinay
Now, Suresh  Vinay = 1.04 Vinay  Vinay
= 0.04 Vinay
= Rs 800 (given)
∴ Vinay = Rs 20000
∴ Vinod = 0.8 x 20000 = Rs 16000
A man sold two watches for Rs. 240 each on one he gained 20% and on the other he lost 20%. The gain or loss percent in the transaction is
S.P. of both the watches = Rs. 480
S.P. of each watch = Rs. 240
Gain = 20%
Two sides of a triangle are 2√2cm and 2√3 cm and the angle opposite to the shorter side of the two is π/4. The largest possible length of the third side is
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
The two trains meet x hrs after 8 a.m.
Distance covered by 1st train in x hrs + Distance covered by 2nd train in (x  1) hrs = 330 km
60x + 75 (x  1) = 330
60x + 75x  75 = 330
x = 405/135 = 3
So, they will meet 3 hrs past 8 a.m. i.e., 11 a.m.
The value of cos 12°+cos 84°+cos 156°+cos 132° is
A milk tanker cylindrical is shape having diameter 2 m and length 4.2 m supplies milk to two booths A and B in the ratio 3:2. Milk booth A is a rectangular vessel having base area as 3.96m^{2} and milk booth B is a cylindrical vessel having diameter 2m. The level of milk in vessels in booths A and B respectively are
Find the minimum number of cubes required to construct a cuboid of dimension 20cm × 16cm × 12cm ?
Volume of cuboid = 20 x 16 x 12 = 3840 cm^{3}
Since minimum no. of cubes required
So length of cube = HCF of 20, 16, 12 cm = 4
The following linegraph gives the percent profit earned by two companies X and Y during the period 19962001. Study the linegraph and answer the questions that are based on it.
Q. If the expenditure of Company Y in 1997 was Rs. 220 crores, what would its income in 1997 ?
Profit perecent of Company Y in 1997 = 35
Let the income of Company Y in 1997 be Rs x crores
⇒ x = 297
∴ Income of Company Y in 1997 = Rs 297 crores
The following linegraph gives the percent profit earned by two companies X and Y during the period 19962001. Study the linegraph and answer the questions that are based on it.
Q. If the incomes of the two companies were equal in 1999, then what was the ratio of expenditure of Comapany X to that of Company Y in 1999 ?
Let the incomes of each of the two Companies X and Y in 1999 be Rs. x.
And let the expenditures of Companies X and Y in 1999 be E1 and E2 respectively.
Then, for Company X we have:
The following linegraph gives the percent profit earned by two companies X and Y during the period 19962001. Study the linegraph and answer the questions that are based on it.
Q. If the expenditure of companies X and Y in 1996 were equal and the total income of the two companies in 1996 was Rs. 342 crores, what was the total profit of the two companies together in 1996 ?
Let the expenditures of each companies X and Y in 1996 be Rs x crores
And let the income of Company X in 1996 be Rs z crores
So that the income of Company Y in 1996 = Rs (342  z) crores
Then, for Company X we have:
Substituting z = 168 in (i), we get : x = 120
∴ Total expenditure of Companies X and Y is 1996 = 2x = Rs 240 crores
Total income of Companies X and Y in 1996 = Rs 342 crores
∴ Total profit = Rs (342  240) crores = Rs 120 crores
The pie charts show estimated revenue and expenditure budgets for 20042005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 20042005 over the estimates for 20032004.
2. Service tax brings in Rs.3990crore according to the budget for 20042005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 20032004 to Rs.7700crore in 20042005.
Q. The revenue generated by Custom duty, Income tax and Corporate tax according to the budget for 20042005 is.
The pie charts show estimated revenue and expenditure budgets for 20042005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 20042005 over the estimates for 20032004.
2. Service tax brings in Rs.3990crore according to the budget for 20042005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 20032004 to Rs.7700crore in 20042005.
Q. What is the percentage increase in the revenue generated by corporate tax is 20042005 over 20032004 according to the budgets?
The pie charts show estimated revenue and expenditure budgets for 20042005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 20042005 over the estimates for 20032004.
2. Service tax brings in Rs.3990crore according to the budget for 20042005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 20032004 to Rs.7700crore in 20042005.
Q. If the percentage distribution for the sectors from he Expenditure graph remain the same for the 20032004 and 20042005 budgets, then what is the difference in budgeted expenditures in 20032004 and 20042005?
The pie charts show estimated revenue and expenditure budgets for 20042005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 20042005 over the estimates for 20032004.
2. Service tax brings in Rs.3990crore according to the budget for 20042005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 20032004 to Rs.7700crore in 20042005.
Q. According to the budget for 20042005, the revenue generated by nondebt capital receipts is what percent of expenditure on subsides?
In the chart given below, A, B,C,D and E represents the costs of paper , printing , binding , miscellaneous and the royalty respectively in publishing a book.
Q. What is the angle of the pie chart showing the expenditure incurred on royalty ?
% of Royalty = 15%
∴ Angle made by Royalty = 360/100 × 15 = 54°
The following linegraph gives the percent profit earned by two companies X and Y during the period 19962001. Study the linegraph and answer the questions that are based on it.
Q. The income of the companies X and Y in 2000 were in the ratio of 3 : 4 respectively. What was the respective ratio of their expenditures in 2000 ?
Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.
And let the expenditures in 2000 of Companies X and Y be E1 and E2 respectively.
Then, for Company X we have:
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