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MATHS 5 Marks Questions

Linear Equations in One Variable · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 41 questions.

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Question 15 Marks
$\text{x}+\frac12=\frac72$
Answer
$\text{x}+\frac12=\frac72$
Subtracting $\frac12$ from both sides, we get
$\text{x}+\frac12-\frac12=\frac72-\frac12$
$\text{x}=\frac72-\frac12=\frac62$
$\text{x}=3$
Verification:
Substituting $x = 3$ is $L.H.S.,$ we get $L.H.S. =3+\frac{6+1}{2}=72$ and $R.H.S. = 72$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 25 Marks
$6x + 5 = 2x + 17$
Answer
We have
$6x + 5 = 2x + 17$
Transposing $2x$ to $L.H.S$. and $5$ to $R.H.S$., we get
$6x - 2x = 17 - 5$
$4x = 12$
Dividing both sides by $4$, we get
$\frac{4\text{x}}{4}=\frac{12}{4}$
$\text{x}=3$
Verification:
Substituting $x = 3$ in the given equation, we get
$6 × 3 + 5 = 2 × 3 + 17$
$18 + 5 = 6 + 17$
$23 = 23$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 35 Marks
$\text{m}-\frac{\text{m}-1}{2}=1-\frac{\text{m}-2}{3}$
Answer
$\text{m}-\frac{\text{m}-1}{2}=1-\frac{\text{m}-2}{3}$
$=\frac{2\text{m}-\text{m}+1}{2}=\frac{3-\text{m}+2}{3}$
$=\frac{\text{m}+1}{2}=\frac{5-\text{m}}{3}$
$=\frac{\text{m}+1}{2}=\frac{5}{3}-\frac{\text{m}}{3}$
$=\frac{\text{m}}{2}+\frac12=\frac53-\frac{\text{m}}{3}$
Transposing $\frac{\text{m}}{3}$ to $L.H.S$. and $\frac12$ to $R.H.S.,$
we get $=\frac{\text{m}}{2}+-\frac{\text{m}}{3}=\frac{5}{3}-\frac12$
$=\frac{3\text{m}+2\text{m}}{6}=\frac{10-3}{6}$ Multiplying both sides by $6,$
we get $=\frac{5\text{m}}{6}\times6=\frac{7}{6}\times6$
$=5\text{m}=7$ Dividing both sides by $5$,
we get $=\frac{5\text{m}}{5}=\frac75$
$=\text{m}=\frac75$ Verification: Substituting $\text{m}=\frac75$ on both sides,
we get $\frac75-\frac{7-5}{10}=1-\frac{7-10}{15}$
$\frac75-\frac{2}{10}=\frac{15+3}{15}$
$\frac{14-2}{10}=\frac{15+3}{15}$
$\frac{12}{10}=\frac{18}{15}$
$\frac{6}{5}=\frac{6}{5}$
$\text{L.H.S.} =\text{R.H.S.}$
Hence, verified.
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Question 45 Marks
$5(x - 2) +3(x + 1) = 25$
Answer
$5(x - 2) + 3(x + 1) = 25$
On expanding the brackets, we get
$(5 × x) - (5 × 2) + 3 × x + 3 × 1 = 25$
$5x - 10 + 3x + 3 = 25$
$5x + 3x - 10 + 3 = 25$
$8x - 7 = 25$
Adding $7$ to both sides, we get
$8x - 7 + 7 = 25 + 7$
$8x = 32$
Dividing both sides by $8$, we get
$\frac{8\text{x}}{8}=\frac{32}{8}$
$\text{x}=4$
Verification:
Substituting $x = 4$ in $L.H.S$., we get
$= 5(4 - 2) + 3(4 + 1) = 5(2) + 3(5) = 10 + 15 = 25 = R.H.S.$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 55 Marks
$\frac45-\text{x}=\frac35$
Answer
$\frac45-\text{x}=\frac35$
Subtracting $\frac45$ from both sides,
we get $\frac{4}{5}-\text{x}-\frac45=\frac35-\frac45$
$-\text{x}=\frac35-\frac45$
$-\text{x}=-\frac15$
Dividing both sides by $-1,$
we get $-\text{x}\times(-1)=-\frac15\times(-1)$
$\text{x}=\frac15$
Verification: Substituting $\text{x}=\frac15$ in
$L.H.S$., we get $\text{L.H.S.}=\frac{4}{5}-\frac15=\frac{4-1}{5}=\frac35,$ and $\text{R.H.S.} = \frac35$
$L.H.S. = R.H.S$. Hence, verified.
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Question 65 Marks
$\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$
Answer
$\frac{\text{x}}{2}=\frac{\text{x}}{3}+1$ Transposing $\frac{\text{x}}{2}$ to $L.H.S.,$
we get $\frac{\text{x}}{2}-\frac{\text{x}}{3}=1$
$\frac{\text{3x}-2\text{x}}{6}=1$
$\frac{\text{x}}{6}=1$ Multiplying both sides by $6,$
we get $\frac{\text{x}}{6}\times6=1\times6$
$\text{x}=6$ Verification: Substituting $x = 6$ in the given equation,
we get $\frac{6}{6}=\frac63+1$
$3=2+1$
$3=3$
$\text{L.H.S.}=\text{R.H.S.}$ Hence, verified.
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Question 75 Marks
$3(x - 3) = 5(2x + 1)$
Answer
$3(x - 3) = 5(2x + 1)$ On expanding the brackets on both sides,
we get $= 3 × x - 3 × 3 = 5 × 2x + 5 × 1 = 3x - 9 = 10x + 5$
Transposing $10x$ to $L.H.S$. and $9$ to $R.H.S.,$
we get $= 3x - 10x = 9 + 5 = -7x = 14$ Dividing both sides by $7,$
we get $=\frac{-7\text{x}}{7}$ $=\frac{-14}{7}$ $=\text{x}=-2$
Verification: Substituting $x = -2$ on both sides,
we get $3(-2 - 3) = 5{2(-2) +1} 3(-5) = 5(-3) -15 = -15 $
$L.H.S. = R.H.S$. Hence, verified.
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Question 85 Marks
$\text{x}-\frac{\text{x}}{4}-\frac{1}{2}=3+\frac{\text{x}}{4}$
Answer
$\text{x}-\frac{\text{x}}{4}-\frac{1}{2}=3+\frac{\text{x}}{4}$
Transposing $\frac{\text{x}}{4}$ to L.H.S. and $-\frac12$ to
$R.H.S$., we get $=\text{x}-\frac{\text{x}}{4}-\frac{\text{x}}{4}=3+\frac12$
$=\frac{4\text{x}-\text{x}-\text{x}}{4}=\frac{6+1}{2}$
$=\frac{2\text{x}}{4}=\frac72$ Multiplying both sides by $4$,
 we get $=\frac{\text{2x}}{4}\times4=\frac72\times4$
$=2\text{x}=14$ Dividing both sides by $2$,
we get $=\frac{\text{2x}}{2}=\frac{14}2{}$
$=\text{x}=7$ Verification: Substituting $x = 7$ on both sides,
we get $7-\frac{7}{4}-\frac12=3+\frac74$
$\frac{2-7-2}{4}=\frac{12+7}{4}$
$=\frac{19}{4}=\frac{19}{4}$
$\text{L.H.S.}=\text{R.H.S.}$ Hence, verified.
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Question 95 Marks
$7 + 4y = - 5$
Answer
$7 + 4y = -5$ Subtracting $7$ from both sides,
we get $7 + 4y - 7 = -5 -7 4y = -12$ Dividing both sides by $4,$
we get $\text{y}=\frac{-12}{4}$ $\text{y}=-3$ Verification: Substituting $y = -3 in L.H.S.,$
we get $L.H.S. = 7 + 4y = 7 + 4(-3) = 7 - 12 = -5,$
and $R.H.S. = -5 L.H.S. = R.H.S.$
Hence, verified.
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Question 105 Marks
$\frac{3}{4}(\text{x}-1)=\text{x}-3$
Answer
$\frac{3}{4}(\text{x}-1)=\text{x}-3$ On expanding the brackets on both sides,
we get $=\frac{\text{3x}}{4}-\frac34=\text{x}-3$
Transposing $\frac34\text{x}$ to $R.H.S$. and $3$ to $L.H.S.,$
we get $\Rightarrow3-\frac34=\text{x}-\frac34\text{x}$
$\Rightarrow\frac{12-3}{4}=\frac{4\text{x}-3\text{x}}{4}$
$\Rightarrow\frac{9}{4}-=\frac{\text{x}}{4}$
Multiplying both sides by $4,$
we get $\Rightarrow\text{x}=9$
Verification: Substituting $x = 9$ on both sides,
we get $\frac{3}{4}(9-1)=9-3$
$\frac34\times8=6$
$L.H.S. = R.H.S$.
Hence, verified.
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Question 115 Marks
$3(x + 2) - 2(x - 1) = 7$
Answer
$3(x + 2) - 2(x - 1) = 7$ On expanding the brackets,
we get $3x + 3 × 2 - 2 × x + 2 × 1 = 7 3x + 6 - 2x + 2 = 7 3x - 2x + 6 + 2 = 7 x + 8 = 7$
Subtracting $8$ from both sides,
we get $x + 8 - 8 = 7 - 8 x = -1$
Verification: Substituting $x = -1$ in $L.H.S.,$
we get $L.H.S. = 3(x + 2) - 2(x - 1) = 3(-1 + 2) - 2(-1 -1) = (3 × 1) - (2 × -2) = 3 + 4 = 7$, and
$R.H.S. = 7 L.H.S. = R.H.S.$
Hence, verified.
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Question 125 Marks
$\frac{\text{5x}-1}{3}-\frac{2\text{x}-2}{3}=1$
Answer
$\frac{\text{5x}-1}{3}-\frac{2\text{x}-2}{3}=1$
$\frac{5\text{x}-1-2\text{x}+2}{3}=1$
$\frac{3\text{x}+1}{3}=1$ Multiplying both sides by $3$,
we get 3 $\frac{3\text{x}+1}{3}\times3=1\times3$
$=\text{3x}+1=3$ Subtracting $1$ from both sides,
we get $= 3x + 1 - 1 = 3 - 1 = 3x = 2$
Dividing both sides by $3$,
we get $= 3x + 1 - 1 = 3 -1 = 3x = 2$
Dividing both sides by $3$,
we get $=\frac{\text{3x}}{3}=\frac{2}{3}$
$=\text{x}=\frac23$ Verification: Substituting $\text{x}=\frac23$ in
$L.H.S$., we get $=\frac{5\big(\frac23\big)-1}{3}-\frac{2\big(\frac23\big)-2}{3}$
$=\frac{\frac{1}3-1}{3}-\frac{\frac43-3}{3}$
$=\frac{\frac{10-3}{3}}{3}-\frac{\frac{4-6}{3}}{3}$
$=\frac{7}{3\times3}-\Big(\frac{-2}{3\times3}\Big)$
$=\frac79+\frac29$
$=\frac99=1=\text{R.H.S.}$
$L.H.S. = R.H.S$. Hence, verified.
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Question 135 Marks
$10 - y = 6$
Answer
$10 - y = 6$ Subtracting $10$ from both sides,
we get $10 - y - 10 = 6 - 10 -y = -4$
Multiplying both sides by $-1,$
we get $-y × -1 = - 4 × - 1 y = 4$
Verification: Substituting $y = 4$ in $L.H.S$.,
we get $L.H.S. = 10 - y = 10 - 4 = 6$ and
$R.H.S. = 6 L.H.S. = R.H.S$.
Hence, verified.
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Question 145 Marks
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
Answer
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
$\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25\text{x}}{100}+7$
$\frac{\text{x}}{2}+\frac{\text{x}}{3}=\frac{\text{x}}{4}+7$
Transposing $\frac{\text{x}}{4}$ to $L.H.S$., we get
$\frac{\text{x}}{2}+\frac{\text{x}}{3}-\frac{\text{x}}{4}=7$
$\frac{65\text{x}+4\text{x}-\text{3x}}{12}=7$
Multiplying both sides by $12$, we get
$\frac{7\text{x}}{12}\times12=7\times12$
$=\text{7x}=84$
Dividing both sides by $7$, we get
$=\frac{7\text{x}}{7}=\frac{84}{7}$
$=\text{x}=12$
Verification:
Substituting $x = 12$ on both sides, we get
$0.5(12) + \frac{12}3 = 0.25(12) + 7$
$6 + 4 = 3 + 7$
$10 = 10$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 155 Marks
$3x - 2(2x - 5) = 2(x + 3) - 8$
Answer
$3x - 2(2x - 5) = 2(x + 3) - 8$
On expanding the brackets on both sides, we get
$= 3x - 2 × 2x + 2 × 5 = 2 × x + 2 × 3 - 8$
$= 3x - 4x + 10 = 2x + 6 - 8$
$= -x + 10 = 2x - 2$
Transposing $x$ to $R.H.S$. and $2$ to $L.H.S.$, we get
$= 10 + 2 = 2x + x$
$= 3x = 12$
Dividing both sides by $3$, we get
$=\frac{3\text{x}}{3}=\frac{12}{3}$
$=\text{x}=4$
Verification:
Substituting $x = 4$ on both sides, we get
$3(4) - 2{2(4) - 5} = 2(4 + 3) - 8$
$12 - 2(8 - 5) = 14 - 8$
$12 - 6 = 6$
$6 = 6$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 165 Marks
$\frac{6\text{x}-2}{9}+\frac{3\text{x}+5}{18}=\frac13$
Answer
$\frac{6\text{x}-2}{9}+\frac{3\text{x+5}}{18}=\frac13$
$=\frac{6\text{x}(2)-2(2)+\text{3x}+5}{18}=\frac13$
$=\frac{12\text{x}-4+3\text{x}+5}{18}=\frac13$
$=\frac{15\text{x}+1}{18}=\frac13$ Multiplying both sides by $18$, we get
$=\frac{15\text{x}+1}{18}\times18=\frac12\times18$
$=15\text{x}+1=6$ Transposing $1$ to
$R.H.S$., we get $= 15x = 6 - 1 = 15x = 5$
Dividing both sides by $15$, we get
$=\frac{15\text{x}}{15}=\frac{5}{15}$
$=\text{x}=\frac13$ Verification: Substituting $\text{x}=\frac13$ both sides,
we get $\frac{6\big(\frac13\big)-2}{9}+\frac{3\big(\frac13\big)+5}{18}=\frac13$
$\frac{2-2}{9}+\frac{1+5}{18}=\frac13$
$0+\frac{6}{18}=\frac13$
$\frac13=\frac13$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 175 Marks
$2\text{y}-\frac12=-\frac13$
Answer
$2\text{y}-\frac12=-\frac{1}{3}$ Adding $\frac12$ to both sides,
we get $\text{2y}-\frac{1}{2}+\frac12=-\frac13+\frac12$
$\text{y}=\frac{-2+3}{6}$
$\text{2y}=\frac{1}{6}$ Dividing both sides by $2$,
we get $\frac{2\text{y}}{2}=\frac{16}{2}$
$\text{y}=\frac{1}{12}$
Verification: Substituting $\text{y}=\frac{1}{12}$ in $L.H.S$. we get
$\text{L.H.S.}=2\frac{1}{12}-\frac12$
$=\frac16-\frac12$
$=\frac{1-3}{6}$
$=\frac{-2}{6}$
$=-\frac{1}{3},$ and R.H.S. $=-\frac13$
$L.H.S. = R.H.S.$
Hence, verified.
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Question 185 Marks
$0.6\text{x}+\frac45=0.28\text{x}+1.16$
Answer
$0.6\text{x} + \frac45 = 0.28\text{x} + 1.16$
Transposing $0.28x$ to $L.H.S$. and $45$ to $R.H.S$., we get 
$ = 0.6x - 0.28x = 1.16 - 45 = 0.32x = 1.16 - 0.8 = 0.32x = 0.36$
 Dividing both sides by $0.32,$ we get 
$ = 0.32 \times 0.32 = 0.360.32 = x = 98$
Verification: Substituting $x = 98$ on both sides, we get 
 $0.6\Big(\frac98\Big) + 45 = 0.28\Big(\frac98\Big) + 1.16$
$\frac{5.4}{8} + \frac45 = \frac{2.52}8 + 1.16$
$0.675 + 0.8 = 0.315 + 1.16$
$1.475 = 1.475$
$L.H.S. = R.H.S$.
Hence, verified.
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Question 195 Marks
$2(5x - 3) - 3(2x - 1) = 9$
Answer
We have $2(5x - 3) - 3(2x - 1) = 9$
Expanding the brackets, we get
$2 \times 5x - 2 \times 3 - 3 \times 2x + 3 \times 1 = 9 10x - 6 - 6x + 3 = 9 10x - 6x - 6 + 3 = 9 4x - 3 = 9$
Adding 3 to both sides, we get $4x - 3 + 3 = 9 + 3 4x = 12$
Dividing both sides by $4$, we get
$\frac{4\text{x}}{4}=\frac{12}{4}$
Thus, $x = 3$. Verification: Substituting $x = 3$ in $L.H.S$., we get
$= 2(5 \times 3 - 3) - 3(2 \times 3 - 1) = 2 \times 12 - 3 \times 5 = 24 - 15 = 9 $
$L.H.S. = R.H.S.$
Hence, verified.
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Question 205 Marks
$\text{x}-\frac{1}{3}=\frac{2}{3}$
Answer
$\text{x}-\frac13=\frac23$ Adding $\frac13$ to both sides, we get
$\text{x}-\frac13+\frac13=\frac23+\frac13$
$\Rightarrow\text{x}=\frac23+\frac13$
$\Rightarrow\text{x}=\frac33$
$\Rightarrow\text{x}=1$
Verification: Substituting $x = 1$ in $L.H.S.,$
we get $\text{L.H.S.}=1-\frac{1}{3}=\frac{3-1}{2}=\frac{2}{3},$ and $\text{R.H.S.}=\frac23$
$\text{L.H.S.}= \text{R.H.S.}$ Hence, verified.
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Question 215 Marks
$\frac{\text{x}}{2}+\frac32=\frac{2\text{x}}{5}-1$
Answer
$\frac{\text{x}}{2}+\frac{3}{2}=\frac{2\text{x}}5-1{}$
Transposing $\frac{2\text{x}}{5}$ to $L.H.S$. and $\frac32$ to $R.H.S$., we get
$=\frac{\text{x}}{2}-\frac{2\text{x}}{5}=-1-\frac32$
$=\frac{5\text{x}-4\text{x}}{10}=\frac{-2-3}{2}$
$=\frac{\text{x}}{10}=\frac{-5}{2}$
Multiplying both sides by $10,$ we get
$=\frac{\text{x}}{10}\times10=\frac{-5}{2}\times10$
$=\text{x}=-25$
Verification: Substituting $x = -25$ in the given equation, we get
$\frac{-25}{2}+\frac32=\frac{2(-25)}{5}-1$
$\frac{-22}{2}=-10-1$
$-11=-11$
$\text{L.H.S.}=\text{R.H.S.}$ Hence, verified.
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Question 225 Marks
$6(1 - 4x) + 7(2 + 5x) = 53$
Answer
$6(1 - 4x) + 7(2 + 5x) = 53$ On expanding the brackets,
we get $(6 \times 1) - (6 \times 4x) + (7 \times 2) + (7 \times 5x) $
$= 53 6 - 24x + 14 + 35x $
$= 53 6 + 14 + 35x - 24x $
$= 53 20 + 11x $
$= 53$
Subtracting $20$ from both sides,
we get $20 + 11x - 20 = 53 - 20 11x = 33$
Dividing both sides by $11,$
we get $\frac{\text{11x}}{11}=\frac{33}{11}$
$\text{x}=3$
Verification: Substituting $x = 3$ in $L.H.S.,$
we get $= 6(1 - 4 \times 3) + 7(2 + 5 \times 3) $
$= 6(1 - 12) + 7(2 + 15) = 6(-11) + 7(17) $
$= -66 + 119 = 53 $
$= R.H.S. L.H.S. $
$= R.H.S.$
Hence, verified.
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Question 235 Marks
$5(2 - 3x) - 17(2x - 5) = 16$
Answer
$5(2 - 3x) - 17(2x - 5) = 16$
On expanding the brackets, we get $(5 \times 2) - (5 \times 3x) - (17 \times 2x) + (17 \times 5) $
$= 16 10 - 15x - 34x + 85 $
$= 16 10 + 85 - 34x - 15x $
$= 16 95 - 49x $
$= 16$
Subtracting 95 from both sides, we get $-49x + 95 - 95 = 16 - 95 -49x = -79$
Dividing both sides by $-49,$
we get $\frac{-49\text{x}}{49}=\frac{-79}{-49}$ $\text{x}=\frac{79}{49}$
Verification: Substituting $\text{x}=\frac{79}{49}$ in $L.H.S.,$
we get $=5\Big(2-3\times\frac{79}{49}\Big)-17\Big(2\times\frac{79}{49}-5\Big)$
$=(5\times2)-\Big(5\times3\times\frac{79}{49}\Big)-\Big(17\times2\times\frac{79}{49}\Big)+(17\times5)$
$=10-\frac{1185}{49}-\frac{2686}{49}+85$
$=\frac{490-1185-2686+4165}{49}=\frac{784}{49}=16=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence, verified.
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Question 245 Marks
$14=\frac{7\text{x}}{10}-8$
Answer
$14=\frac{7\text{x}}{10}-8$ Adding $8$ to both sides,
we get $14+8=\frac{7\text{x}}{10}-8+8$
$22=\frac{7\text{x}}{10}$ Multiplying both sides by $10$,
we get $22\times10=\frac{7\text{x}}{10}\times10$
$220=7\text{x}$ Dividing both sides by $7,$
we get $\frac{220}{7}=\frac{7\text{x}}{7}$
$\text{x}=\frac{220}{7}$
Verfication: Substituting $\text{x}=\frac{220}{7}$ $R.H.S$.,
we get $L.H.S. = 14$ and $\text{R.H.S.}=\frac{\frac{220}{7}}{\frac{7}{10}}10-8$
$=\frac{220}{10}-8$
$=22-8=14$
$L.H.S. = R.H.S$. Hence, verified.
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Question 255 Marks
$8(2x - 5) - 6(3x - 7) = 1$
Answer
$8(2x - 5) - 6(3x - 7) = 1$ On expanding the brackets, we get $(8 × 2x) - (8 × 5) - (6 × 3x) + (-6) × (-7) = 1$
$16x - 40 - 18x + 42 = 1$
$16x - 18x + 42 - 40 = 1$
$-2x + 2 = 1$
Subtracting $2$ from both sides, we get
$-2x+ 2 - 2 = 1 - 2$
$-2x = -1$
Multiplying both sides by $-1$, we get
$-2x × (-1) = -1 × (-1)$
$2x = 1$
Dividing both sides by $2$, we get
$\frac{2\text{x}}{2}=\frac12$
$\text{x}=\frac12$
Verification:
Substituting $\text{x}=\frac12$ in $L.H.S.$, we get
$=8\Big(2\times\frac{1}{2}-5\Big)-6\Big(3\times\frac{1}{2}-7\Big)$
$= 8(1 - 5) - 6(32 - 7)$
$= 8× (-4) - (6 \times 32) + (6 \times 7) $
$= -32 - 9 + 42 $
$= - 41 + 42 = 1 = \text{R.H.S.}$
$\text{L.H.S.} = \text{R.H.S.}$
Hence, verified.
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Question 265 Marks
$\frac{\text{x}-3}{5}-2=-1$
Answer
$\frac{\text{x}-3}{5}-2=-1$ Adding $2$ to both sides, 
we get $\frac{\text{x}-3}{5}-2+2=-1+2$
$\frac{\text{x}-3}{5}=1$ Multiplying both sides by $5, $
we get $\frac{\text{x}-3}{5}\times5=1\times5$
$\text{x}-3=5$ Adding $3$ to both sides, 
we get $x - 3 + 3 = 5 + 3 x = 8$
Verification: Substituting $x = 8$ in $L.H.S., $
we get $=\frac{8-3}{5}-2=\frac{5}{5}-2=1-2=-1=\text{R.H.S.}$
Hence, verified.
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Question 275 Marks
$\frac{1}{3}-\text{2x}=0$
Answer
$\frac{1}{3}-\text{2x}=0$ Subtracting $13$ from both sides,
we get $\frac{1}{3}-2\text{x}-\frac13=0-\frac13$ $-2\text{2x}=-\frac13$
Multiplying both sides by $-1$,
we get $-2\text{x}\times(-1)=-\frac{1}{3}\times(-1)$ $2\text{x}=\frac13$
Dividing both sides by $2$, we get $\frac{2\text{x}}{2}=\frac{\frac13}{2}$ $\text{x}=\frac16$
Verification: Substituting $\text{x}=\frac16$ in
$L.H.S.$, we get $\text{L.H.S.}=\frac13-2\times\frac16=\frac13-\frac13=0,$ and $\text{R.H.S.}=0$
$\text{L.H.S.}=\text{R.H.S.}$
​​​​​​​Hence Verified.
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Question 285 Marks
A man is 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find the their present ages.
Answer
Son: 8 years, Man 32 years
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Question 295 Marks
Mrs. Jain is 27 years older than her daughter Nilu. After 8 years she will be twice as old as Nilu. Find their present ages.
Answer
Nilu: 19 years, Mrs. Jain: 46 years
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Question 305 Marks
Shikha is 3 years younger to her brother Ravish. If the sum of their ages is 37 years, what are their present ages?
Answer
Shikha: 17 years, Ravish 20 years
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Question 325 Marks
A man says, "I am thinking of a number. When I divide it by 3 and then add 5 , my answer is twice the number I thought of". Find the number.
Answer
3
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Question 335 Marks
The difference between two numbers is 7 . Six times the smaller plus the larger is 77 . Find the numbers.
Answer
10, 17
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Question 345 Marks
Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.
Answer
16, 17, 18
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Question 355 Marks
In a hostel mess, 50 kg rice are consumed everyday. If each student gets 400 gm of rice per day, find the number of students who take meals in the hostel mess.
Answer
125
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Question 365 Marks
There are only 25 paise coins in a purse. The value of money in the purse is $₹ 17.50$. Find the number of coins in the purse.
Answer
70
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Question 375 Marks
The length of a rectangular field is twice its breadth. If the perimeter of the field is 228 metres, find the dimensions of the field.
Answer
Length $=76$ metres, Breadth $=38$ metres
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Question 385 Marks
A bag contains 25 paise and 50 paise coins whose total value is $₹ 30$. If the number of 25 paise coins is four times that of 50 paise coins, find the number of each type of coins.
Answer
50 paise coins : 20,25 paise coins : 80
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Question 395 Marks
Andy has twice as many marbles as Pandy, and Sandy has half as many has Andy and Pandy put together. If Andy has 75 marbles more than Sandy. How many does each of them have?
Answer
Pandy: 150 Marbles, Andy: 300 Marbles Sandy: 225 Marbles,
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Question 405 Marks
One day, during their vacation at a beach resort, Shella found twice as many sea shells as Anita and Anita found 5 shells more than Sandy. Together Sandy and Shella found 16 sea shells. How many did each of them find?
Answer
Sandy: 2 , Anita: 7 , Shella: 14
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Question 415 Marks
The difference in age between a girl and her younger sister is 4 years. The younger sister in turn is 4 years older than her brother. The sum of the ages of the younger sister and her brother is 16 . How old are the three children?
Answer
Brother: 6 years, Younger sister: 10 years, Girl: 14 years.
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