Question 13 Marks
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is 4 and the remainder is 2. Find the numbers.
Answer19, 13
[Hint. $3 x=4 y+5$ and $6 y=4 x+2$.]
View full question & answer→Question 23 Marks
If from twice the greater of the two numbers, 45 is subtracted, the result is the other number. If from twice the smaller number, 21 is subtracted, the result is the greater number. Find the numbers.
Question 33 Marks
Find two numbers such that the sum of twice the first and thrice the second is 103 and four times the first exceeds seven times the second by 11.
Question 43 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 53 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 63 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 73 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 83 Marks
There are two examination halls A and B. If 12 pupils are sent from A to B, the number of pupils in each room becomes the same. If 11 pupils are sent from room B to room A, then the number of pupils in A is double their number in B. Find the number of pupils in each room.
AnswerA = 81 pupils, B = 57 pupils
View full question & answer→Question 93 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.
Answer6 litres, 15 litres
[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.]
View full question & answer→Question 103 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 113 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 123 Marks
A number of two digits exceeds four times the sum of its digits by 6 and the number is increased by 9 on reversing the digits. Find the number.
Question 133 Marks
When a two-digit number is divided by the sum of its digits, the quotient is 8. On diminishing the ten's digit by three times the unit's digit, the remainder obtained is 1. Find the number.
Answer72
[Hint. Let the ten's digit be $x$ and unit's digit be $y$. Then, $\frac{10 x+y}{x+y}=8$ and $x-3 y=1$.]
View full question & answer→Question 143 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 153 Marks
A number consists of two digits, the difference of whose digits is 5. If 8 times the number is equal to 3 times the number obtained by reversing the digits, find the number.
Question 163 Marks
A number consists of two digits, the difference of whose digits is 3 . If 4 times the number is equal to 7 times the number obtained by reversing the digits, find the number.
Answer63
[Hint. Original number is greater than the number obtained by reversing its digits. $\therefore$ In original number, ten's digit is greater than unit's digit.]
View full question & answer→Question 173 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 183 Marks
The sum of two numbers is 53 and their difference is 25. Find the numbers.
Question 193 Marks
Solve the equation:
$\frac{x}{7}+\frac{y}{3}=5, \frac{x}{2}-\frac{y}{9}=6$
View full question & answer→Question 203 Marks
Solve the equation:
$\frac{x+y-8}{2}=\frac{x+2 y-14}{3}=\frac{3 x+y-12}{11}$
View full question & answer→Question 213 Marks
Solve the equation:
$4 x-3 y=8,18 x-3 y=29$
Answer$x =\frac{3}{2}, y=\frac{-2}{3}$
View full question & answer→Question 223 Marks
Solve the equation:
$\frac{7-4 x}{3}=y, 2 x+3 y+1=0$
View full question & answer→Question 233 Marks
Solve the equation:
$7 x-2 y=20,11 x+15 y+23=0$
View full question & answer→Question 243 Marks
Solve the equation:
$10 x+3 y=75,6 x-5 y=11$
View full question & answer→Question 253 Marks
Solve the equation:
$x+2 y+9=0,3 x+4 y+17=0$
View full question & answer→Question 263 Marks
Solve the equation:
The sides of an equilateral triangle are $(x+3 y) cm ,(3 x+2 y-2) cm$ and $\left(4 x+\frac{y}{2}+1\right)$ cm . Find the length of each side.
Answer15 cm
[Hint. $x+3 y=3 x+2 y-2=4 x+\frac{y}{2}+1$.
The solution gives $x=3$ and $y=4$.
Each side of the triangle $=(x+3 y) cm =(3+12) cm =15 cm$.]
View full question & answer→Question 273 Marks
Solve the equation:
If $2 x+y=32$ and $3 x+4 y=68$, find the value of $\frac{x}{y}$.
View full question & answer→Question 283 Marks
Solve the equation:
$\frac{a}{x}-\frac{b}{y}=0, \frac{a b^2}{x}+\frac{a^2 b}{y}=\left(a^2+b^2\right)$
View full question & answer→Question 293 Marks
Solve the equation:
$23 x-29 y=98,29 x-23 y=110$.
Answer$x=3, y=-1$
[Hint. Add \& Subtract the given equations]
View full question & answer→Question 303 Marks
Solve the equation:
$103 x+51 y=617 \ldots$ (i),
$97 x+49 y=583 \ldots$ (ii)
Answer$x=5, y=2$
[Hint. Add (i) and (ii) Subtract (ii) from (i)]
View full question & answer→Question 313 Marks
Solve the equation:
$\frac{22}{x+y}+\frac{15}{x-y}=5, \frac{55}{x+y}+\frac{40}{x-y}=13$
View full question & answer→Question 323 Marks
Solve the equation:
$5 x+4 y=4, x-12 y=20$
Answer$x=2, y=\frac{-3}{2}$
View full question & answer→Question 333 Marks
Solve the equation:
$\frac{3}{x+y}+\frac{2}{x-y}=3, \frac{2}{x+y}+\frac{3}{x-y}=\frac{11}{3}$
Answer$x=2, y=1$
\[\left[\text { Hint. Put } \frac{1}{x+y}=u \text { and } \frac{1}{x-y}=v\right]\]
View full question & answer→Question 343 Marks
Solve the equation:
$x+y=2 x y, x-y=6 x y$
Answer$x=\frac{-1}{2}, y=\frac{1}{4}$
[Hint. Divide each throughout by $x y$ ]
View full question & answer→Question 353 Marks
Solve the equation:
$\frac{3}{2 x}+\frac{2}{3 y}=5, \frac{5}{x}-\frac{3}{y}=1$
Answer$x=\frac{1}{2}, y=\frac{1}{3}$
[ Hint. Put $\frac{1}{x}=u$ and $\frac{1}{y}=v$]
View full question & answer→Question 363 Marks
Solve the equation:
$\frac{2}{x}+\frac{2}{3 y}=\frac{1}{6}, \frac{3}{x}+\frac{2}{y}=0$
Answer$x=6, y=-4$
\[\left[\text { Hint. Put } \frac{1}{x}=u \text { and } \frac{1}{y}=v\right]\]
View full question & answer→Question 373 Marks
Solve the equation:
$5 x-9=\frac{1}{y}, x+\frac{1}{y}=3$
View full question & answer→Question 383 Marks
Solve the equation:
$4 x+\frac{6}{y}=15,3 x-\frac{4}{y}=7$
View full question & answer→Question 393 Marks
Solve the equation:
$\frac{7+x}{5}-\frac{2 x-y}{4}=3 y-5, \frac{4 x-3}{6}+\frac{5 y-7}{2}=18-5 x$
View full question & answer→Question 403 Marks
Solve the equation:
$\frac{x}{2}+y=\frac{4}{5}, x+\frac{y}{2}=\frac{7}{10}$
Answer$x=\frac{2}{5}, y=\frac{3}{5}$
View full question & answer→Question 413 Marks
Solve the equation:
$4 x+\frac{x-y}{8}=17, x+2 y=\frac{y-2}{3}-2$
View full question & answer→Question 423 Marks
Solve the equation:
$\frac{x}{6}+6=y, \frac{3 x}{4}=1+y$
View full question & answer→Question 433 Marks
Solve the equation:
$x+2 y=1,3 x-y=17$
View full question & answer→Question 443 Marks
A number of two digits exceeds four times the sum of its digits by 6 and the number is increased by 9 on reversing the digits. Find the number.
Question 453 Marks
When a two-digit number is divided by the sum of its digits, the quotient is 8. On diminishing the ten's digit by three times the unit's digit, the remainder obtained is 1. Find the number.
[Hint. Let the ten's digit be $x$ and unit's digit be $y$. Then, $\frac{10 x+y}{x+y}=8$ and $x-3 y=1$ ]
View full question & answer→Question 463 Marks
A number consists of two digits, the difference of whose digits is 5. If 8 times the number is equal to 3 times the number obtained by reversing the digits, find the number.
Question 473 Marks
A number consists of two digits, the difference of whose digits is 3. If 4 times the number is equal to 7 times the number obtained by reversing the digits, find the number.
[Hint. Original number is greater than the number obtained by reversing its digits.
$\therefore$ In original number, ten's digit is greater than unit's digit.]
View full question & answer→Question 483 Marks
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is 4 and the remainder is 2. Find the numbers.
[Hint. 3x = 4y + 5 and 6y = 4x + 2.]
Question 493 Marks
If from twice the greater of the two numbers, 45 is subtracted, the result is the other number. If from twice the smaller number, 21 is subtracted, the result is the greater number. Find the numbers.
Question 503 Marks
Find two numbers such that the sum of thrice the first and the second is 142 and four times the first exceeds the second by 138.