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AlgebraQuestion and Answers: Page 255

Question Number 104419    Answers: 2   Comments: 0

Now the sum of your father and your is 90 years. 5 years ago your father′s age was 3 times than your age. Write the your age and your father′s age 3 years after.

$$\boldsymbol{\mathrm{Now}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{is}} \\ $$$$\mathrm{90}\:\boldsymbol{\mathrm{years}}.\:\mathrm{5}\:\boldsymbol{\mathrm{years}}\:\boldsymbol{\mathrm{ago}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{age}} \\ $$$$\boldsymbol{\mathrm{was}}\:\mathrm{3}\:\boldsymbol{\mathrm{times}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{age}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{age}}\:\mathrm{3}\:\boldsymbol{\mathrm{years}} \\ $$$$\boldsymbol{\mathrm{after}}. \\ $$

Question Number 104413    Answers: 2   Comments: 0

The sum of two integers is 304 and their GCD is 19. What are the numbers?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{integers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{304} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{is}}\:\mathrm{19}.\:\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{numbers}}? \\ $$

Question Number 104410    Answers: 1   Comments: 0

If 11×11=121, 111×111=12321,1111×1111=1234321 then what is the answer of 111111×111111 ? (It is a short question)

$$\boldsymbol{\mathrm{If}}\:\mathrm{11}×\mathrm{11}=\mathrm{121}, \\ $$$$\mathrm{111}×\mathrm{111}=\mathrm{12321},\mathrm{1111}×\mathrm{1111}=\mathrm{1234321} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{answer}}\:\boldsymbol{\mathrm{of}} \\ $$$$\mathrm{111111}×\mathrm{111111}\:? \\ $$$$\left(\boldsymbol{\mathrm{It}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{short}}\:\boldsymbol{\mathrm{question}}\right) \\ $$

Question Number 104404    Answers: 1   Comments: 0

(4/5)=(?/(45))=((20)/?)=((144)/?)=((200)/?)

$$\frac{\mathrm{4}}{\mathrm{5}}=\frac{?}{\mathrm{45}}=\frac{\mathrm{20}}{?}=\frac{\mathrm{144}}{?}=\frac{\mathrm{200}}{?} \\ $$

Question Number 104391    Answers: 0   Comments: 1

(x−a)(x−b)(x−c)....(x−z) = ?

$$\left(\boldsymbol{{x}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{c}}\right)....\left(\boldsymbol{{x}}−\boldsymbol{{z}}\right)\:=\:? \\ $$

Question Number 104394    Answers: 1   Comments: 0

Question Number 104377    Answers: 1   Comments: 6

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 .... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{196}\:\:\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:....\:\left(\mathrm{iii}\right) \\ $$

Question Number 104369    Answers: 1   Comments: 0

Question Number 104326    Answers: 1   Comments: 2

Suppose you had x rupees. Your father gave you more 6 rupees. You gave y rupees to your brother. Now how many rupees you have? You will buy three shirts with the rupees that you have now. Write the cost of each shirt.

$$\boldsymbol{\mathrm{Suppose}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{Your}} \\ $$$$\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{gave}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{more}}\:\mathrm{6}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{You}} \\ $$$$\boldsymbol{\mathrm{gave}}\:\boldsymbol{{y}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{brother}}.\:\boldsymbol{\mathrm{Now}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}?\:\boldsymbol{\mathrm{You}}\:\boldsymbol{\mathrm{will}} \\ $$$$\boldsymbol{\mathrm{buy}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{shirts}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{now}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{cost}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{each}} \\ $$$$\boldsymbol{\mathrm{shirt}}. \\ $$

Question Number 104297    Answers: 1   Comments: 0

((3a^2 b^3 c)/(5b^4 c))+((6xy^3 z^(16) )/(10x^2 y^2 z^(10) )) = ? Can you solve this?

$$\frac{\mathrm{3}{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}}{\mathrm{5}{b}^{\mathrm{4}} {c}}+\frac{\mathrm{6}{xy}^{\mathrm{3}} {z}^{\mathrm{16}} }{\mathrm{10}{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{10}} }\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104294    Answers: 1   Comments: 0

1. ((1(1/2)+2(6/7))/(2(2/3)−3(4/5)))=? 2. 4×Π×Π=? 3. Transfer into fractions: 5.8^. 9^. , 9.6^. , 78.57^. 8^.

$$\mathrm{1}.\:\:\frac{\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}\frac{\mathrm{6}}{\mathrm{7}}}{\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}−\mathrm{3}\frac{\mathrm{4}}{\mathrm{5}}}=? \\ $$$$\mathrm{2}.\:\:\mathrm{4}×\Pi×\Pi=? \\ $$$$\mathrm{3}.\:\:\boldsymbol{\mathrm{Transfer}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fractions}}: \\ $$$$\:\:\:\:\:\:\mathrm{5}.\overset{.} {\mathrm{8}}\overset{.} {\mathrm{9}},\:\mathrm{9}.\overset{.} {\mathrm{6}},\:\mathrm{78}.\mathrm{5}\overset{.} {\mathrm{7}}\overset{.} {\mathrm{8}} \\ $$

Question Number 104278    Answers: 1   Comments: 0

x−(−(−x+(−x+x)))= ?

$${x}−\left(−\left(−{x}+\left(−{x}+{x}\right)\right)\right)=\:? \\ $$

Question Number 104260    Answers: 0   Comments: 1

You bought 3g rice, 5g flour in a market. At first you had 500 rupees. Now you have 300 rupees. How much rupees you wasted? Suppose you distribute the 300 rupees among your 4 sons. Now how much rupees does your one son get?

$$\mathrm{You}\:\mathrm{bought}\:\mathrm{3g}\:\mathrm{rice},\:\mathrm{5g}\:\mathrm{flour}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{market}.\:\mathrm{At}\:\mathrm{first}\:\mathrm{you}\:\mathrm{had}\:\mathrm{500}\:\mathrm{rupees}. \\ $$$$\mathrm{Now}\:\mathrm{you}\:\mathrm{have}\:\mathrm{300}\:\mathrm{rupees}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{rupees}\:\mathrm{you}\:\mathrm{wasted}?\:\mathrm{Suppose}\:\mathrm{you} \\ $$$$\mathrm{distribute}\:\mathrm{the}\:\mathrm{300}\:\mathrm{rupees}\:\mathrm{among} \\ $$$$\mathrm{your}\:\mathrm{4}\:\mathrm{sons}.\:\mathrm{Now}\:\mathrm{how}\:\mathrm{much}\:\mathrm{rupees} \\ $$$$\mathrm{does}\:\mathrm{your}\:\mathrm{one}\:\mathrm{son}\:\mathrm{get}? \\ $$

Question Number 104253    Answers: 1   Comments: 1

When a∗b= ((a+b)/(a−b)) then what is the answer of 2∗3×9∗10 ?

$$\mathrm{When}\:{a}\ast{b}=\:\frac{{a}+{b}}{{a}−{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:? \\ $$

Question Number 104251    Answers: 1   Comments: 0

If x=8 and y=5 then what is the answer of ((x+y+6)/(x^2 −y^3 )) ?

$$\mathrm{If}\:{x}=\mathrm{8}\:\mathrm{and}\:{y}=\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\:\frac{{x}+{y}+\mathrm{6}}{{x}^{\mathrm{2}} −{y}^{\mathrm{3}} }\:? \\ $$

Question Number 104246    Answers: 3   Comments: 0

(1−(1/3))(1−(1/4))(1−(1/5))....(1−(1/(99))) =?

$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)....\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{99}}\right)\:=? \\ $$

Question Number 104243    Answers: 2   Comments: 0

prove that π=2×(2/(√2))×(2/(√(2+(√2))))×(2/(√(2+(√(2+(√2))))))×.....

$${prove}\:{that} \\ $$$$\pi=\mathrm{2}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}}×..... \\ $$

Question Number 104270    Answers: 1   Comments: 0

sgn(∣x∣)=?

$${sgn}\left(\mid{x}\mid\right)=? \\ $$

Question Number 104235    Answers: 1   Comments: 0

If you are given a triangle with side length 15 , 20 and 25. what is the triangle′s shortest altitude?

$${If}\:{you}\:{are}\:{given}\:{a}\:{triangle} \\ $$$${with}\:{side}\:{length}\:\mathrm{15}\:,\:\mathrm{20}\:{and} \\ $$$$\mathrm{25}.\:{what}\:{is}\:{the}\:{triangle}'{s} \\ $$$${shortest}\:{altitude}? \\ $$

Question Number 104201    Answers: 0   Comments: 0

If a^2 + b^2 + c^2 = 1 and b + ic = (1 + a)z, then show that ((a + ib)/(i + c)) = ((1 + iz)/(1 − iz))

$$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{b}\:\:+\:\:\mathrm{ic}\:\:=\:\:\left(\mathrm{1}\:\:+\:\:\mathrm{a}\right)\mathrm{z}, \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\:\frac{\mathrm{a}\:\:+\:\:\mathrm{ib}}{\mathrm{i}\:\:+\:\:\mathrm{c}}\:\:\:=\:\:\:\frac{\mathrm{1}\:\:+\:\:\mathrm{iz}}{\mathrm{1}\:\:−\:\:\mathrm{iz}} \\ $$

Question Number 104190    Answers: 3   Comments: 1

integers x,y satisfy 2x+15y=2019. find the minimum of ∣y−x∣.

$${integers}\:{x},{y}\:{satisfy}\:\mathrm{2}{x}+\mathrm{15}{y}=\mathrm{2019}. \\ $$$${find}\:{the}\:{minimum}\:{of}\:\mid{y}−{x}\mid. \\ $$

Question Number 104115    Answers: 1   Comments: 0

Question Number 104086    Answers: 1   Comments: 3

Solve: log_r 8 + log_3 p = 5 ..... (i) r + p = 11 ..... (ii)

$$\mathrm{Solve}:\:\:\:\:\:\:\mathrm{log}_{\mathrm{r}} \mathrm{8}\:\:\:+\:\:\:\mathrm{log}_{\mathrm{3}} \mathrm{p}\:\:\:=\:\:\mathrm{5}\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{r}\:\:\:+\:\:\mathrm{p}\:\:\:=\:\:\mathrm{11}\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$

Question Number 104062    Answers: 3   Comments: 4

{ (((x/y) + (y/x) = ((13)/6))),((x+y = 5)) :} find the solution

$$\begin{cases}{\frac{{x}}{{y}}\:+\:\frac{{y}}{{x}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}}\\{{x}+{y}\:=\:\mathrm{5}}\end{cases} \\ $$$${find}\:{the}\:{solution} \\ $$

Question Number 104037    Answers: 4   Comments: 0

(1) { ((x^3 +y^6 = 91)),((x+y^2 = 7 )) :} find x−y^6 . (2) 2a+(2/a) = 8 ⇒ ((a^6 +1)/a^3 ) ?

$$\left(\mathrm{1}\right)\begin{cases}{{x}^{\mathrm{3}} +{y}^{\mathrm{6}} \:=\:\mathrm{91}}\\{{x}+{y}^{\mathrm{2}} \:=\:\mathrm{7}\:}\end{cases} \\ $$$${find}\:{x}−{y}^{\mathrm{6}} \:. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{a}+\frac{\mathrm{2}}{{a}}\:=\:\mathrm{8}\:\Rightarrow\:\frac{{a}^{\mathrm{6}} +\mathrm{1}}{{a}^{\mathrm{3}} }\:? \\ $$

Question Number 104023    Answers: 0   Comments: 1

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