Question 14 Marks
A man travels 600 km partly by train and partly by car. If he covers 120 km by train and the rest by car, it takes him 8 hours. But, if he travels 200 km by train and the rest by car, he takes 20 minutes longer. Find the speed of the car and that of the train.
Question 24 Marks
If 11 pens and 19 pencils together cost ₹ 502; while 19 pens and 11 pencils together cost ₹ 758, how much 3 pens and 6 pencils cost together?
Question 34 Marks
The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 12 less than twice the original number. Find the original number.
Question 44 Marks
Find the fraction which becomes $\frac{1}{2}$ when its numerator is increased by 6 and is equal to $\frac{1}{3}$ when its denominator is increased by 7 .
View full question & answer→Question 54 Marks
Solve the following systems of equation by using the method of cross multiplication:
$a x+b y=(a-b), b x-a y=(a+b)$
View full question & answer→Question 64 Marks
Solve the following systems of equation by using the method of cross multiplication:
$7 x-2 y=20,11 x+15 y+23=0$
View full question & answer→Question 74 Marks
Solve the following systems of equation by using the method of cross multiplication:
$8 x-3 y=12,5 x=2 y+7$
View full question & answer→Question 84 Marks
Solve the following systems of equation by using the method of cross multiplication:
$2 x+5 y=1,2 x+3 y=3$
View full question & answer→Question 94 Marks
Solve the following systems of equation by using the method of cross multiplication:
$x+2 y+1=0,2 x-3 y=12$
View full question & answer→Question 104 Marks
Solve the following systems of equation by using the method of cross multiplication:
$2 x+3 y=17,3 x-2 y=6$
View full question & answer→Question 114 Marks
Solve the following systems of equation by using the method of cross multiplication:
$3 x-5 y=19,7 x-3 y=1$
View full question & answer→Question 124 Marks
Solve the following systems of equation by using the method of cross multiplication:
$5 x-4 y+2=0,2 x+3 y=13$
View full question & answer→Question 134 Marks
$\frac{5}{x+1}-\frac{2}{y-1}=\frac{1}{2}, \frac{10}{x+1}+\frac{2}{y-1}=\frac{5}{2}$, where $x \neq-1$ and $x \neq 1$
Answer$x=4, y=5$
$\left[\right.$ Hint. Put $\frac{1}{x+1}=u$ and $\left.\frac{1}{y-1}=v\right]$
View full question & answer→Question 144 Marks
$\frac{10}{x+y}+\frac{2}{x-y}=4, \frac{15}{x+y}-\frac{5}{x-y}+2=0$, where $x \neq y$ and $x \neq-y$
View full question & answer→Question 154 Marks
Solve the following systems of equation by using the method of cross multiplication:
$\frac{1}{x}+\frac{1}{y}=7, \frac{2}{x}+\frac{3}{y}=17(x \neq 0, y \neq 0)$
Answer$x=\frac{1}{4}, y=\frac{1}{3}$
View full question & answer→Question 164 Marks
Solve the following systems of equation by using the method of cross multiplication:
$\frac{5}{x}-\frac{4}{y}+2=0, \frac{2}{x}+\frac{3}{y}=13(x \neq 0, y \neq 0)$
Answer$x=\frac{1}{2}, y=\frac{1}{3}$
View full question & answer→Question 174 Marks
Solve the following systems of equation by using the method of cross multiplication:
$3 x+2 y+25=0,2 x+y+10=0$
View full question & answer→Question 184 Marks
Solve the following systems of equation by using the method of cross multiplication:
$2 x-5 y+8=0, x-4 y+7=0$
View full question & answer→Question 194 Marks
The angles of a triangle in ascending order are $x, y$ and z . If $y-x=z-y=10$, then find the angles of the triangle.
Answer$50^{\circ}, 60^{\circ}, 70^{\circ}$
View full question & answer→Question 204 Marks
A shopkeeper buys pens and pencils at 5 and 1 per piece respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12% and 10% profit, respectively. If his total sale is ₹ 725, then find the number of pens and pencils sold by him.
Question 214 Marks
A boatman rowing at the rate of 5 km/h in still water takes thrice as much time in going 40 km upstream as in going 40 km downstream. What is the speed of the stream?
Question 224 Marks
A shopkeeper sold a table and a chair for ₹ 1050, thereby making a profit of 10% on the table and 25% on the chair. If he had taken a profit of 25% on the table and 10% on the chair, then he would have got ₹ 1065. What is the cost price of 1 table and 1 chair.
Question 234 Marks
A and B together can do a piece of work in 6 days. If A's one day's work be $1 \frac{1}{2}$ times the one day's work of B, find in how many days, each alone can finish the work.
View full question & answer→Question 244 Marks
A lady has 25-P and 50-P coins in her purse. If in all she has 80 coins totalling ₹ 25, how many coins of each kind does she have?
Answer25-P coins = 60, 50-P coins = 20
View full question & answer→Question 254 Marks
6 men and 8 boys can finish a piece of work in 14 days while 8 men and 12 boys can do it in 10 days. Find the time taken by one man alone and that by one boy alone to finish the work.
Answer1 man can do it in 140 days and 1 boy can do it in 280 days.
View full question & answer→Question 264 Marks
A man travels 600 km partly by train and partly by car. If he covers 120 km by train and the rest by car, it takes him 8 hours. But, if he travels 200 km by train and the rest by car, he takes 20 minutes longer. Find the speed of the car and that of the train.
Question 274 Marks
A man sold a chair and a table for ₹ 2178, thereby making a profit of 12% on the chair and 16% on the table. By selling them for ₹ 2154, he gains 16% on the chair and 12% on the table. Find the cost price of each.
AnswerTable - ₹ 1250, chair - ₹ 650
View full question & answer→Question 284 Marks
A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Find the quantity of each of the solutions to get the resultant mixture.
[Hint. Let x litres of 90% solution be mixed with y litres of 97% acid solution.
Then, x + y = 21 and 90% of x + 97% of y = 95% of 21.]
Question 294 Marks
The monthly incomes of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 3 : 2. If each saves ₹ 1500 per month, find their monthly incomes.
Question 304 Marks
5 kg sugar and 7 kg rice together cost ₹ 258, while 7 kg sugar and 5 kg rice together cost ₹ 246. Find the total cost of 8 kg sugar and 10 kg rice.
Question 314 Marks
If 11 pens and 19 pencils together cost ₹ 502; while 19 pens and 11 pencils together cost ₹ 758, how much 3 pens and 6 pencils cost together?
Question 324 Marks
The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 12 less than twice the original number. Find the original number.
Question 334 Marks
The result of dividing a number of two digits by a number with digits reversed is $1 \frac{3}{4}$. If the sum of the digits is 12 , find the number.
View full question & answer→Question 344 Marks
A fraction becomes $\frac{1}{2}$ when 1 is subtracted from its numerator and 1 is added to its denominator. Also, it becomes $\frac{1}{3}$ when 6 is subtracted from its numerator and 1 from the denominator. Find the original fraction.
View full question & answer→Question 354 Marks
Find the fraction which becomes $\frac{1}{2}$ when its numerator is increased by 6 and is equal to $\frac{1}{3}$ when its denominator is increased by 7 .
View full question & answer→Question 364 Marks
Solve the following systems of equations by using the method of cross multiplication:
$\frac{5}{x+1}-\frac{2}{y-1}=\frac{1}{2}, \frac{10}{x+1}+\frac{2}{y-1}=\frac{5}{2}$, where $x \neq-1$ and $x \neq 1$
$\left[\right.$ Hint. Put $\frac{1}{x+1}=u$ and $\left.\frac{1}{y-1}=v\right]$
View full question & answer→Question 374 Marks
Solve the following systems of equations by using the method of cross multiplication:
$\frac{10}{x+y}+\frac{2}{x-y}=4, \frac{15}{x+y}-\frac{5}{x-y}+2=0$, where $x \neq y$ and $x \neq-y$
View full question & answer→Question 384 Marks
Solve the following systems of equations by using the method of cross multiplication:
$\frac{1}{x}+\frac{1}{y}=7, \frac{2}{x}+\frac{3}{y}=17(x \neq 0, y \neq 0)$
Answer$x=\frac{1}{4}, y=\frac{1}{3}$
View full question & answer→Question 394 Marks
Solve the following systems of equations by using the method of cross multiplication:
$\frac{5}{x}-\frac{4}{y}+2=0, \frac{2}{x}+\frac{3}{y}=13(x \neq 0, y \neq 0)$
Answer$x=\frac{1}{2}, y=\frac{1}{3}$
View full question & answer→Question 404 Marks
Solve the following systems of equations by using the method of cross multiplication:
3x + 2y + 25 = 0, 2x + y + 10 = 0
Question 414 Marks
Solve the following systems of equations by using the method of cross multiplication:
ax + by = (a - b), bx - ay = (a + b)
Question 424 Marks
Solve the following systems of equations by using the method of cross multiplication:
7x - 2y = 20, 11x + 15y + 23 = 0
Question 434 Marks
Solve the following systems of equations by using the method of cross multiplication:
8x - 3y = 12, 5x = 2y +7
Question 444 Marks
Solve the following systems of equations by using the method of cross multiplication:
2x + 5y = 1, 2x + 3y = 3
Question 454 Marks
Solve the following systems of equations by using the method of cross multiplication:
x + 2y + 1 = 0, 2x - 3y = 12
Question 464 Marks
Solve the following systems of equations by using the method of cross multiplication:
2x + 3y = 17, 3x - 2y = 6
Question 474 Marks
Solve the following systems of equations by using the method of cross multiplication:
3x - 5y = 19, 7x - 3y = 1
Question 484 Marks
Solve the following systems of equations by using the method of cross multiplication:
5x - 4y + 2 = 0, 2x + 3y = 13
Question 494 Marks
Solve the following systems of equations by using the method of cross multiplication:
2x - 5y + 8 = 0, x - 4y + 7 = 0