5 Marks Questions - Maths STD 7 Questions - Vidyadip

Questions

5 Marks Questions

Take a timed test

21 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks

Solve the following equations. Check your result in case. $2\text{x}-\frac{1}{3}=\frac{1}{5}-\text{x}$

Answer

$2\text{x}-\frac{1}{3}=\frac{1}{5}-\text{x}$
$\Rightarrow2\text{x}+\text{x}=\frac{1}{5}+\frac{1}{3}$ (By transposing)
$\Rightarrow3\text{x}=\frac{3+5}{15}$
$\Rightarrow3\text{x}=\frac{8}{15}$
$\Rightarrow\text{x}=\frac{8}{15}\times\frac{1}{3}=\frac{8}{45}$
$\text{x}=\frac{8}{45}$ Check: $\text{L.H.S.}=2\text{x}-\frac{1}{3}$
$=2\times\frac{8}{45}-\frac{1}{3}=\frac{16}{45}-\frac{1}{3}$
$=\frac{16-15}{45}=\frac{1}{45}$
$\text{R.H.S}.=\frac{1}{5}-\text{x}=\frac{1}{5}-\frac{8}{45}$
$=\frac{9-8}{45}=\frac{1}{45}$
$\therefore\text{L.H.S.}=\text{R.H.S.}$ Hence $\text{x}=\frac{8}{45}$

View full question & answer→

Question 25 Marks

The ages of Sonal and Manoj are in the ratio $7 : 5$ Ten years hence, the ratio of their ages will be $9 : 7$. Find their present ages.

Answer

Ratio in present ages of Sonal and Manoj $= 7 : 5$
Let Sonal’s age $= 7x$
then Manoj’s age $= 5x 10$ years hence,
Sonal’s age will be $= 7x + 10$ And
Manoj’s age $= 5x + 10$
$\therefore\frac{7\text{x}+10}{5\text{x}+10}=\frac{9}{7}$ (By cross multiplications)
$7(7\text{x}+10)=9(5\text{x}+10)$
$\Rightarrow49\text{x}+70=45\text{x}+90$
$\Rightarrow49\text{x}-45\text{x}=90-70$
$\Rightarrow4\text{x}=20$
$\Rightarrow\text{x}=\frac{20}{4}=5$
Sonal’s present age $= 7x = 7 \times 5 = 35$
years And Manoj’s age $ = 5x = 5 \times 5 = 25$ years

View full question & answer→

Question 35 Marks

Solve the following equations. Check your result in case. $6(3x + 2) - 5(6x - 1) = 3(x - 8) - 5(7x - 6) + 9x$

Answer

$6(3x + 2) - 5(6x - 1) = 3(x - 8) - 5(7x - 6) + 9x $
$\Rightarrow 18x + 12 - 30x + 5 = 3x - 24 - 35x + 30 + 9x $
$\Rightarrow 18x - 30x + 12 + 5 = 3x - 35x + 9x - 24 + 30 $
$\Rightarrow -12x + 17 = -23x + 6 $
$\Rightarrow -12x + 23x = 6 - 17 $
$\Rightarrow 11x = -11 x = -1$
Check: $L.H.S. = 6(3x + 2) - 5(6x - 1) = 6[3x (-1) + 2] - 5[6x (-1) \times -1] = 6[-3 + 2] - 5[-6 - 1] $
$= 6x (-1) - 5 \times (-7) = -6 + 35 = 29 $
$R.H.S. = 3(x - 8) - 5(7x - 6) + 9x = 3[-1 - 8] - 5[7x(-1) - 6] + 9(-1) = 3x(-9) - 5[-7 - 6] - 9 $
$= -27 - 5(-13) - 9 = -27 + 65 - 9 = 65 - 36 = 29$
$L.H.S. = R.H.S.$
Hence $x = -1$

View full question & answer→

Question 45 Marks

Solve the following equations. Check your result in case. $\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}=1$

Answer

$\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}=1$
$\frac{4(\text{y}-1)-3(\text{y}-2)}{12}=1$ (LCM of $3, 4 = 12)$
$\Rightarrow\frac{4\text{y}-4-3\text{y}+6}{12}=1$
$\Rightarrow\frac{\text{y}+2}{12}=1$
$\Rightarrow\text{y}+2=12$
$\Rightarrow\text{y}=12-2=10$
$\Rightarrow\text{y}=10$
Check: $\text{L.H.S.}=\frac{\text{y}-1}{3}-\frac{\text{y}-2}{4}$
$=\frac{10-1}{3}-\frac{10-2}{4}$
$=\frac{9}{3}-\frac{8}{4}=3-2$
$=1$
$=\text{R.H.S. = L.H.S.}$ Hence $= \text{y}=10$

View full question & answer→

Question 55 Marks

Solve the following equations. Check your result in case.
$\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}=3$

Answer

$\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}=3$
$\Rightarrow\frac{6(\text{x}-9)+7\text{x}=63}{21}$ $(LCM$ of $7, 3 = 21)$
$\Rightarrow6\text{x}-54+7\text{x}=63$
$\Rightarrow6\text{x}+7\text{x}=63+54=117$
$\Rightarrow13\text{x}=117$
$\Rightarrow\text{x}=\frac{117}{13}=9$
Check:
$\text{L.H.S.}=\frac{2}{7}(\text{x}-9)+\frac{\text{x}}{3}$
$=\frac{2}{7}(9-9)+\frac{9}{3}$
$=\frac{2}{7}\times0+3$
$=0+3=3\text{ R.H.S.}$
Hence $\text{x}=9$

View full question & answer→

Question 65 Marks

Solve the following equations. Check your result in case. $t - (2t + 5) - 5(1 - 2t) = 2(3 + 4t) - 3(t - 4)$

Answer

$t - (2t + 5) - 5(1 - 2t) = 2(3 + 4t) - 3(t – 4) $
$ t - 2t - 5 - 5 + 10t = 6 + 8t - 3t + 12t $
$ t - 2t + 10t - 10 = 8t - 3t + 18 $
$ 9t - 10 = 5t + 18 $
$ 9t - 5t = 18 + 10$ (By transposing)
$ 4t = 28 $
$ t = 7$
Check: L.H.S. $
$= t - [2t + 5] - 5[1 - 2t] $
$= 7 - [2 \times 7 + 5] - 5[1 - 2 \times 7] $
$= 7 - [14 + 5] - 5[1 - 14] $
$= 7 - 19 - 5(-13) $
$= 7 - 19 + 65 $
$= 72 - 19 $
$= 53 R.H.S. $
$= 2[3 + 4t) - 3(t - 4) $
$= 2(3 + 4 \times 7) - 3(7 – 4) $
$= 2(3 + 28) - 3(3) $
$= 2(31) - 9 $
$= 62 - 9 $
$= 53 L.H.S. $
$= R.H.S. Hence t $
$= 7$

View full question & answer→

Question 75 Marks

Solve the following equations. Check your result in case. $\frac{\text{y}+7}{3}=1+\frac{3\text{y}-2}{5}$

Answer

$\frac{\text{y}+7}{3}=1+\frac{3\text{y}-2}{5}$
$\frac{5(\text{y}+7)=15+3(3\text{y}-2)}{15}$
($LCM$ of $3, 5 = 15)$ $5\text{y}+35=15+9\text{y}-6$
$5\text{y}-9\text{y}=15-6-25$ (By transposing) $-4\text{y}=-26$
$\text{y}=\frac{-26}{-4}=\frac{13}{2}$
$\therefore\text{y}=\frac{13}{2}$
Check: $\text{L.H.S.}=\frac{\text{y}-7}{3}=\frac{\frac{13}{2}+7}{3}$
$=\frac{13+14}{2\times3}$
$=\frac{27}{6}=\frac{9}{2}$
$\text{R.H.S.}=1+\frac{3\text{y}-2}{5}$
$=1+\frac{3\times\frac{13}{2}-2}{5}$
$=1+\frac{\frac{39}{2}-\frac{2}{1}}{5}$
$=1+\frac{39-4}{2\times5}$
$=1+\frac{35}{10}$
$=1+\frac{7}{2}=\frac{2+7}{2}=\frac{9}{2}$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{y}=\frac{13}{2}$

View full question & answer→

Question 85 Marks

Solve the following equations. Check your result in case. $\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}=\frac{4\text{x}+1}{7}$

Answer

$\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}=\frac{4\text{x}+1}{7}$
$\frac{28(2\text{x}-3)+35(\text{x}+3)=20(4\text{x}+1)}{140}$
$(LCM$ of $5, 4, 7 = 140)$ $28(2\text{x}-3)+35(\text{x}+3)=20(4\text{x}+1)$
$\Rightarrow56\text{x}-84+35\text{x}+105=80\text{x}+20$
$\Rightarrow56\text{x}+35\text{x}-80\text{x}=20+84-105$
$\Rightarrow91\text{x}-80\text{x}=140-105$
$\Rightarrow11\text{x}=-1$
$\Rightarrow\text{x}=\frac{-1}{11}$
$\therefore\text{x}=\frac{-1}{11}$
Check: $\text{L.H.S.}=\frac{2\text{x}-3}{5}+\frac{\text{x}+3}{4}$
$=\frac{2\Big(-\frac{1}{11}\Big)-3}{5}+\frac{\frac{-1}{11}+3}{4}$
$=\frac{\frac{-2}{11}-3}{5}+\frac{\frac{-1}{11}+3}{4}$
$=\frac{-2-33}{11\times5}+\frac{-1+33}{11\times4}$
$=\frac{-35}{11\times5}+\frac{32}{11\times4}$
$=\frac{-7}{11}+\frac{8}{11}$
$=\frac{1}{11}$
$\text{R.H.S}.=\frac{4\text{x}+1}{7}$
$=\frac{4\Big(-\frac{1}{11}\Big)+1}{7}$
$=\frac{-\frac{4}{11}+1}{7}$
$=\frac{-4+11}{11\times7}$
$=\frac{7}{11\times7}$
$=\frac{1}{11}$
$\text{L.H.S. = R.H.S.}$

View full question & answer→

Question 95 Marks

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

Answer

Five years ago, Let Son’s age $= x$
years And father’s age $= 7x$
years Present age of son $= (x + 5)$
years And age of father $= (7x + 5)$
years $5$ years hence, Father’s age $= 7x + 5 + 5 = 7x + 10$ And
Son’s age $= x + 5 + 5 = x + 10 (7x + 10) = 3(x + 10) $
$\Rightarrow 7x + 10 = 3x + 30 $
$\Rightarrow 7x – 3x = 30 - 10 $
$\Rightarrow 4x = 20 $
$\Rightarrow x = 5$
Father present age $= 7x + 5 = 7 x 5 + 5 = 35 + 5 = 40$ years And
son’s age $= x + 5 = 5 + 5 = 10$ years

View full question & answer→

Question 105 Marks

Solve the following equations. Check your result in case. $\frac{\text{x}+2}{6}-\Big(\frac{11-\text{x}}{3}-\frac{1}{4}\Big)=\frac{3\text{x}-4}{12}$

Answer

$\frac{\text{x}+2}{6}-\Big(\frac{11-\text{x}}{3}-\frac{1}{4}\Big)=\frac{3\text{x}-4}{12}$
$\frac{\text{x}+2}{6}-\Big(\frac{11-\text{x}}{3}+\frac{1}{4}\Big)=\frac{3\text{x}-4}{12}$
$\frac{2(\text{x}+2)-4(11-\text{x})+3=3\text{x}-4}{12}$ $(LCM$ of $6, 3, 4, 12 = 12)$
$\Rightarrow2\text{x}+4-44+4\text{x}+3=3\text{x}-4$
$\Rightarrow2\text{x}+4\text{x}-3\text{x}=-4-4+44-3$
$\Rightarrow6\text{x}-3\text{x}=44-11$
$\Rightarrow3\text{x}=33$
$\Rightarrow\text{x}=\frac{33}{3}=11$
$\therefore\text{x}=11$
check: $\text{L.H.S.}=\frac{\text{x}+2}{6}-\Big[\frac{11\times\text{x}}{3}-\frac{1}{4}\Big]$
$=\frac{11+2}{6}-\Big[\frac{11-11}{3}-\frac{1}{4}\Big]$
$=\frac{13}{6}-\Big(0-\frac{1}{4}\Big)$
$=\frac{13}{6}=\frac{1}{4}$
$=\frac{26+3}{12}=\frac{29}{12}$
$\text{R.H.S.}=\frac{3\text{x}-4}{12}=\frac{3\times11-4}{12}$
$=\frac{33-4}{12}=\frac{29}{12}$
$\because\text{L.H.S. = R.H.S.}$ Hence $\text{x}=11$

View full question & answer→

Question 115 Marks

Solve the following equations. Check your result in case. $\frac{3}{4}(7\text{x}-1)-\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\text{x}+\frac{3}{2}$

Answer

$\frac{3}{4}(7\text{x}-1)-\Big(2\text{x}-\frac{1-\text{x}}{2}\Big)=\text{x}+\frac{3}{2}$
$\Rightarrow\frac{3(7\text{x}-1)}{4}-\frac{4\text{x}-1+\text{x}}{2}=\frac{2\text{x}+3}{2}$
$\Rightarrow\frac{21\text{x}-3}{4}-\frac{5\text{x}-1}{2}=\frac{2\text{x}+3}{2}$
$=\frac{21\text{x}-3-10\text{x}+2=4\text{x}+6}{4}$ $(LCM 4, 2 = 4)$
$\Rightarrow21\text{x}-10\text{x}-4\text{x}=6+3-2$ (By transposing)
$\Rightarrow7\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{7}=1$
$\therefore\text{x}=1$
Check: $\frac{3}{4}(7\text{x}-1)-\Big[2\text{x}-\frac{1-\text{x}}{2}\Big]$
$=\frac{3}{4}(7\times1-1)-\Big[2\times1-\frac{1-1}{2}\Big]$
$=\frac{3\times6}{4}-(2-0)=\frac{18}{4}-2$
$=\frac{9}{2}-2=\frac{9-4}{2}=\frac{5}{2}$
$\text{R.H.S.}=\text{x}+\frac{3}{2}$
$=1+\frac{3}{2}$
$=\frac{2+3}{2}=\frac{5}{2}$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=1$

View full question & answer→

Question 125 Marks

Solve the following equations. Check your result in case. $\frac{9\text{x}+7}{2}-\Big(\text{x}-\frac{\text{x}-2}{7}\Big)=36$

Answer

$\frac{9\text{x}+7}{2}-\Big(\text{x}-\frac{\text{x}-2}{7}\Big)=36$
$\Rightarrow\frac{9\text{x}+7}{2}-\frac{\text{x}}{1}+\frac{\text{x}-2}{7}=36$
$\Rightarrow\frac{7(9\text{x}+7)-14\text{x}+2(\text{x}-2)=36\times14}{14}$ $(LCM$ of $2, 7 = 14)$
$\Rightarrow63+49-14\text{x}+2\text{x}-4=504$
$\Rightarrow63\text{x}-14\text{x}+2\text{x}=504+4-49$
$\Rightarrow65\text{x}-14\text{x}=508-49$
$\Rightarrow51\text{x}=459$
$\Rightarrow\text{x}=\frac{459}{51}=9$
$\therefore\text{x}=9$
Check: $\text{L.H.S.}=\frac{9\text{x}+7}{2}-\Big(\text{x}-\frac{\text{x}-2}{7}\Big)$
$=\frac{9\times9\times7}{2}-\Big(9-\frac{9-2}{7}\Big)$
$=\frac{81+7}{2}-\Big(9-\frac{7}{7}\Big)$
$=\frac{88}{2}-(9-1)$
$=44-8$
$\text{R.H.S.}=36$
$\text{R.H.S. = L.H.S.}$
Hence $\text{x}=9$

View full question & answer→

Question 135 Marks

Solve the following equations. Check your result in case. $\frac{\text{x}-2}{4}+\frac{1}{3}=\text{x}-\frac{2\text{x}-1}{3}$

Answer

$\frac{\text{x}-2}{4}+\frac{1}{3}=\frac{\text{x}}{1}-\frac{2\text{x}-1}{3}$
$\frac{3(\text{x}-2)+4=12\text{x}-4(2\text{x}-1)}{12}$ $(LCM$ of $4, 3 = 12)$
$3(\text{x}-2)+4=12\text{x}-4(2\text{x}-1)$
$\Rightarrow3\text{x}-6+4=12\text{x}-8\text{x}+4$
$\Rightarrow3\text{x}-12\text{x}+8\text{x}=4+6-4$
$\Rightarrow-12\text{x}+11\text{x}=10-4$
$\Rightarrow-\text{x}=6$
$\Rightarrow\text{x}=-6$
$\therefore\text{x}=-6$
Check: $\text{L.H.S.}=\frac{\text{x}-2}{4}+\frac{1}{3}$
$=\frac{-6-2}{4}+\frac{1}{3}=\frac{-8}{4}+\frac{1}{3}$
$=-2+\frac{1}{3}$
$=\frac{-6+1}{3}=-\frac{5}{3}$
$\text{R.H.S.}=\text{x}-\frac{2\text{x}-1}{3}$
$=-6-\frac{2(-6)-1}{3}$
$=-6-\frac{-12-1}{3}=-6-\frac{(-13)}{3}$
$=-6+\frac{13}{3}=\frac{-18+13}{3}=-\frac{5}{3}$
$\therefore\text{ L.H.S.= R.H.S.}$
Hence $\text{x}=-6$

View full question & answer→

Question 145 Marks

A number consists of two digits whose sum is $8.$ If $18$ is added to the number its digits are reversed. Find the number.

Answer

Sum of digits $= 8$
Let units digit $= x$
Then tens digit $= 8 - x$ and number will be $x + 10 (8 - x) ….(i)$ By adding $18,$
the digits are reversed then units digit $= 8 - x$ and
tens digit $= x$
Number $= (8 - x) = 10x$
According to the condition, $(8 - x) + 10x = 18 + x + 10 (8 - x) $
$\Rightarrow 8 - x + 10x = 18 + x + 80 - 10x $
$\Rightarrow 10x - x - x + 10x = 18 + 80 - 8 $
$\Rightarrow 18x = 90 $
$\Rightarrow x = 5$
Number is $x + 10(8 - x) $
$= 5 + 10(8 - 5) $
$= 5 + 10 \times 3 = 35$

View full question & answer→

Question 155 Marks

Solve the following equations. Check your result in case.
$\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=3$

Answer

$\frac{21\text{x}-7-5\text{x}}{35}=\frac{3}{1}$ $(LCM$ of $5, 7 = 35)$
$\frac{16\text{x}-7}{35}=\frac{3}{1}$ (By cross multiplication)
$\Rightarrow16\text{x}-7=3\times35$
$\Rightarrow16\text{x}-7=105$
$\Rightarrow16\text{x}=105+7=112$
$\Rightarrow\text{x}=\frac{112}{6}=7$
$\Rightarrow\text{x}=7$
$\therefore\text{x}=7$
Check:
$\text{L.H.S.}=\frac{3\text{x}-1}{5}-\frac{\text{x}}{7}=\frac{3\times7-1}{5}=\frac{-7}{7}$
$=\frac{21-1}{5}-1=\frac{20}{5}-1=4-1=3=\text{R.H.S.}$
Hence $\text{x}=7$

View full question & answer→

Question 165 Marks

Solve the following equations. Check your result in case. $0.18(5x - 4) = 0.5x + 0.8$

Answer

$0.18(5\text{x} - 4) = 0.5\text{x} + 0.8$
$\frac{18}{100}(5\text{x}-4)=\frac{5}{10}\text{x}+\frac{8}{10}$
$\frac{18(5\text{x}-4)=50\text{x}+80}{100}$
$\Rightarrow90\text{x}-72=50\text{x}+80$
$\Rightarrow90\text{x}-50\text{x}=80+72$
$\Rightarrow40\text{x}=152$
$\Rightarrow\text{x}=\frac{152}{40}=\frac{38}{10}=3.8$
$\therefore\text{x}=3.8$
Check: $L.H.S. = 0.18(5x - 4) = 0.18(5 \times 3.8 - 4)$
$= 0.18(19.0 - 4)$
$= 0.18 \times 15 = 2.70$
$= 2.7 R.H.S.$
$= 0.5x + 0.8$
$= 0.5 \times 3.8 + 0.8$
$= 1.90 + 0.8$
$= 1.9 + 0.8$
$= 2.7$
$\because L.H.S. = R.H.S.$
Hence $x = 3.8$

View full question & answer→

Question 175 Marks

Solve the following equations. Check your result in case.
$2\text{x}-3=\frac{3}{10}(5\text{x}-12)$

Answer

$\frac{3\text{x}-3}{1}=\frac{3}{10}(5\text{x}-12)$
$\Rightarrow10(2\text{x}-3)=3(5\text{x}-12)$ (By cross multiplication)
$\Rightarrow20\text{x}-30=15\text{x}-36$
$\Rightarrow20\text{x}-15\text{x}=-36+30$
$\Rightarrow5\text{x}=-6$
$\Rightarrow\text{x}=\frac{-6}{5}$
$\therefore\text{x}=\frac{-6}{5}$
Check
$\text{L.H.S.}=2\text{x}-3=2\times\Big(\frac{-6}{5}\Big)-3$
$=\frac{-12}{5}-\frac{3}{1}=\frac{-12-15}{5}=\frac{-27}{5}$
$\text{R.H.S.}=\frac{3}{10}(5\text{x}-12)$
$=\frac{3}{10}\Big[5\text{x}\Big(\frac{-6}{5}\Big)-12\Big]$
$=\frac{3}{10}(-6-12)=\frac{3}{10}\times(-18)$
$\frac{3\times(-18)}{10}=\frac{3\times(-9)}{5}=\frac{-27}{5}$
$\therefore\text{L.H.S.=R.H.S.}$
Hence $\text{x}=\frac{-6}{5}$

View full question & answer→

Question 185 Marks

Solve the following equations. Check your result in case. $0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$

Answer

$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
$\Rightarrow\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25}{100}\text{x}+7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{\text{x}}{3}=\frac{\text{x}}{4}=7$
$\Rightarrow\frac{1}{2}\text{x}+\frac{1}{3}\text{x}-\frac{1}{4}\text{x}=7$
$\Rightarrow\frac{6\text{x}+4\text{x}-3\text{x}}{12}=7$
$\Rightarrow\frac{7\text{x}}{12}=7$
$\Rightarrow\text{x}=\frac{7\times12}{7}=12$
$\therefore\text{x}=12$
Check: $\text{L.H.S.}=0.5\text{x}+\frac{\text{x}}{3}$
$=\frac{1}{2}\text{x}+\frac{\text{x}}{3}$
$=\frac{12}{2}+\frac{12}{3}$
$=6+4$
$=10$
$\text{R.H.S.}=0.25\text{x}+7$
$=\frac{1}{4}\times12+7$
$=3+7$
$=10$
$\therefore\text{L.H.S. = R.H.S.}$
Hence $\text{x}=12$

View full question & answer→

Question 195 Marks

Solve the following equations. Check your result in case. $\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}=\frac{1}{3}$

Answer

$\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}=\frac{1}{3}$
$=\frac{5(2\text{x}-1)-3(6\text{x}-2)}{5}=\frac{1}{3}$ $(LCM$ of $3, 5 = 15)$
$10\text{x}-5-18\text{x}+6=5$
$\Rightarrow-8\text{x}+1=5$
$\Rightarrow-8\text{x}=5-1=4$
$\therefore\text{x}=\frac{4}{-8}=\frac{-1}{2}$
Check: $\text{L.H.S.}=\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}$
$=\frac{2\times\Big(-\frac{1}{2}\Big)-1}{3}-\frac{6\times\Big(-\frac{1}{2}\Big)-2}{5}$
$=\frac{-1-1}{3}-\frac{-3-3}{5}=\frac{-2}{3}-\frac{(-15)}{5}$
$=\frac{-2}{3}+1=\frac{1}{3}=\text{R.H.S.}$
Hence $\text{x}=\frac{-1}{2}$

View full question & answer→

Question 205 Marks

Hari Babu left one-third of his property to his son, one-fourth to his daughter and the remainder to his wife. If his wife’s share is $Rs. 18000$, what was the worth of his total property?

Answer

Let the worth of hari babu's property be $Rs x$.
According to the question,
We have Son's share $=\frac{1}{4}\text{x}$
Daughter's share $=\frac{1}{3}\text{x}$
Wife's share $=\Big\{\text{x}-\Big(\frac{1}{4}\text{x}+\frac{1}{3}\text{x}\Big)\Big\}$ It is
given that his wife's share is$ Rs. 18000$.
i.e, $\text{x}-\Big(\frac{1}{4}\text{x}+\frac{1}{3}\text{x}\Big)=18000$
$\Rightarrow\text{x}-\Big(\frac{1}{3}\text{x}+\frac{1}{4}\text{x}\Big)=18000$
$\Rightarrow\text{x}-\frac{7\text{x}}{12}=18000$
$\Rightarrow\frac{5\text{x}}{12}=18000$
$\Rightarrow\text{x}=\frac{10000^{36000}\times12}{5}$
$\Rightarrow\text{x}=43200$
$\therefore$ Hari babu's total property is worth $Rs. 43200.$

View full question & answer→

Question 215 Marks

Solve the following equations. Check your result in case. $\frac{2}{3}\text{x}=\frac{3}{8}\text{x}+\frac{7}{12}$

Answer

$\frac{2}{3}\text{x}=\frac{3}{8}\text{x}+\frac{7}{12}$
$\Rightarrow\frac{2}{3}\text{x}-\frac{3}{8}\text{x}=\frac{7}{12}$ (By transposing)
$\Rightarrow\frac{16\text{x}-9\text{x}}{24}=\frac{7}{12}$ ($LCM$ of $3, 8 = 24)$
$\Rightarrow\frac{7\text{x}}{24}=\frac{7}{12}$
$\Rightarrow\text{x}=\frac{7}{12}\times\frac{24}{7}=2$
$\therefore\text{x}=2$
Check: $\text{L.H.S.}=\frac{2}{3}\text{x}=\frac{2}{3}\times2=\frac{4}{3}$
$\text{R.H.S.}=\frac{3}{8}\text{x}+\frac{7}{12}$
$=\frac{3}{8}\times2+\frac{7}{12}=\frac{3}{4}+\frac{7}{12}$
$=\frac{9+7}{12}=\frac{16}{12}=\frac{4}{3}$
$\therefore\text{L.H.S.=R.H.S.}$
Hence $\text{x}=2$

View full question & answer→

Generate Paper Free All Linear Equations in One Variable topics