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Now, $(14\frac{6}{7}+15\frac{2}{7} - 5\frac{2}{3}\times3\frac{1}{2}=?)$

$(\begin{array}{l} = \frac{{104}}{7} + \frac{{107}}{7} - \frac{{17}}{3} \TIMES \frac{7}{2}\\ = \frac{{211}}{7} - \frac{{119}}{6} \end{array})$

$(\begin{array}{l} = \frac{{1266\;-\;833}}{{42}}\\ = \frac{{433}}{{42}}\\ =\;?=10\frac{{13}}{{42}} \end{array})$

GIVEN expression,

⇒ 3^2X + 3^X = 3^x + 3

⇒ 3^2x = 3

⇒ 2x = 1

∴ REQUIRED % = {(155.2 – 97)/ 97} × 100 = 60%

a is 7 TIMES longer than B.

⇒ a = 7b

The percentage by which b is LESS than a = [(a – b)/a] × 100 = [(7b – b)/7b] × 100 = (6/7) × 100 ≈ 86%

∴ The percentage by which b is less than a = 86%

GIVEN expression:

73% of 650 – 111% of 240

⇒ [73% of 650] – [111% of 240]

$(\RIGHTARROW \LEFT[ {\frac{{73}}{{100}} \TIMES 650\left] - \right[\frac{{111}}{{100}} \times 240} \right])$

⇒ [73 × 6.5] – [111 × 2.4]

⇒ 474.5 – 266.4 = 208.1

(18 + 2 × 3.3) + 0.003

= (18 + 6.6) + 0.003

= 24.6 + 0.003

Let x = $(\sqrt {7 + \sqrt {7 + \sqrt {7 +\ldots } } })$

⇒ $({\RM{x}} = \sqrt {7 + {\rm{x}}})$

⇒ x² = 7 + x

⇒ x² – x – 7 = 0

Hence we get,

$({\rm{x}} = \frac{{1 \PM \sqrt {1 + 28} }}{2} = \frac{{1 \pm 5.385}}{2} = 3.1925,{\rm{\;}} - 2.1925)$

Since, the GIVEN term is positive,

Follow BODMAS rule to solve this question, as per the order given below,

Step–1: PARTS of an equation enclosed in 'Brackets' must be SOLVED first, and in the bracket,

Step–2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step–3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step–4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

[3357 ÷ 9 + {(34 × 4 – 67) ÷ 3 + 24}] – 27 = ? × 5 + 4 × 67

⇒ [3357 ÷ 9 + {69 ÷ 3 + 24}] – 27 = ? × 5 + 4 × 67

⇒ [3357 ÷ 9 + {69 ÷ 3 + 24}] – 27 = ? × 5 + 4 × 67

⇒ [373 + 47] – 27 = ? × 5 + 268

⇒ 420 – 27 – 268 = ? × 5

⇒ ? = 125/5

1/6 of 7842 + 125% of X = 3342

⇒ 1/6 × 7842 + 125/100 × x = 3342

⇒ 1307 + 5/4 × x = 3342

⇒ 5/4 × x = 3342 – 1307

⇒ x = 2035 × 4/5 = 1628

Given expression is,

(51.01 ÷ 16.84) + 20.90 = 35.85 – ?

We can write the given VALUES as:

51.01 ≈ 51 and 16.84 ≈ 17

20.90 ≈ 21 and 35.85 ≈ 36

Then,

⇒ (51 ÷ 17) + 21 = 36 – ?

⇒ 3 + 21 = 36 – ?

⇒ 24 = 36 – ?

⇒ ? = 36 – 24

Follow BODMAS RULE to solve this question, as per the order GIVEN below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, the BODMAS rule must be followed,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are CALCULATED,

Step-4-Last but not least, the parts of the equation that ?contain 'Addition' and 'Subtraction' should be calculated.

4015 × 73 - 21817 = ? × 112 + 126

⇒ 293095 - 21817 = ? × 112 + 126

⇒ 271278 = ? × 112 + 126

⇒ ? × 112 = 271278 - 126

⇒ ? = 271152/112

$(\SQRT {69696} = 264)$

LET the NUMBER be x

Wrong number = 11x/13

Actual number = 13x/11

ERROR = 13x/11 – 11x/13 = 48x/143

⇒ $(\left( {\sqrt {9604} \DIV \sqrt {2401} } \RIGHT) \times \left( {\sqrt {2500} - \sqrt {64} } \right))$ = $(\left( {98 \div 49} \right) \times \left( {50\; - 8} \right))$ = 2 × 42 = 84

In this type of question, we are expected to calculate Approximate VALUE (not exact value), so we can replace the given numbers by their nearest perfect places which makes the calculation easy.

Let, 24.95 ≈ 25, 9.88 ≈ 10, 1010 ≈1000, 624 ≈625, 51 ≈ 50 and 499 ≈ 500

Now, given EXPRESSION:

$(\Rightarrow {\left( {\FRAC{{25}}{{10}}} \right)^2} \times \frac{{1000}}{{625}} + \frac{{50}}{{500}} = ?)$

$(\Rightarrow {\RM{\;}}? = {\left( {\frac{{25}}{{10}}} \right)^2} \times \frac{{1000}}{{625}} + \frac{{50}}{{500}})$

$(\Rightarrow {\rm{\;}}? = \frac{{625}}{{100}} \times \frac{{1000}}{{625}} + \frac{{50}}{{500}})$

⇒ ? = 10 + 0.1

⇒ ? = 10.1

369.01 ÷ 9.03 + 123.98 ÷ 4.01 + 1460 × 1.25 = ?

Approximating the value to the NEAREST integer:

⇒ 369 ÷ 9 + 124 ÷ 4 + 1460 × (5/4) = ?

$( \Rightarrow \FRAC{{369}}{9} + \frac{{124}}{4} + 1460 \times \frac{5}{4} = {\rm{}}?)$

⇒ 41 + 31 + 1825 = 1897

Approximating the numbers in the above EXPRESSION:

⇒ (350 × 10) ÷ 7 + 1245 = ?

⇒ 3500 ÷ 7 + 1245 = ?

⇒ 500 + 1245 = ?

SUM of RECIPROCALS of 6/5 and 3/7 = 5/6 + 7/3 = 5/6 + 14/6 = 19/6

Reciprocal of sum of reciprocals of 6/5 and 3/7 = 6/19

⇒ X^Z = y²

⇒ z = 140/48 = 35/12

⇒ 10^(0.48z) = 10^{(2 x 0.70)} = 10^1.40

⇒ 0.48 z = 1.40

⇒ z = 140/48 = 35/12

⇒ z = 2.9

335 × 335 – 165 × 165

⇒ 335² – 165²

⇒ (335 + 165) (335 – 165)

⇒ 500 × 170

⇒ 15.8 × 3 + 8.1 – 21.5 = ? + 14.6

⇒ 47.4 + 8.1 – 21.5 = ? + 14.6

⇒ ? + 14.6 = 34

x = 1 + √6 + √7

$(\BEGIN{ARRAY}{l}x + \FRAC{1}{{x - 1}}\\ = \left( {1 + \sqrt 6+ \sqrt 7 } \right) + \frac{1}{{1 + \sqrt 6+ \sqrt 7- 1}}\\ = 1 + \sqrt 6+ \sqrt 7+ \frac{1}{{\sqrt 6+ \sqrt 7 }} \TIMES \frac{{\sqrt 6- \sqrt 7 }}{{\sqrt 6- \sqrt 7 }}\;\\ = 1 + \sqrt 6+ \sqrt 7+ \frac{{\left( {\sqrt 6- \sqrt 7 } \right)}}{{6 - 7}}\end{array})$

= 1 + √6 + √7 + √7 – √6

Follow BODMAS rule to solve this question, as PER the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are CALCULATED,

Step-4- LAST but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

17.94% of 250 + √2810 - 23.87% of 350 = ?

Taking the approximate values as,

17.94 ≈ 18, √2810 ≈ √2809, 23.87 ≈ 24

⇒ 18% of 250 + √2809 - 24% of 350 = ?

⇒ 0.18 × 250 + 53 - 0.24 × 350 = ?

⇒ 45 + 53 - 84 = ?

$(\frac{{\SQRT[3]{{64}} \TIMES \sqrt {121} }}{{\sqrt {289}- \sqrt {169} }} = \frac{{\sqrt[3]{{4 \times 4 \times 4\;}} \times \sqrt {11 \times 11} }}{{\sqrt {17 \times 17}- \sqrt {13 \times 13} }} = \frac{{4\; \times \;11}}{{17 - \;13}} = \frac{{44}}{4} = 11\;)$

Let us solve each of the square roots INDIVIDUALLY:

√196 = 14

14 + 130 = 144

√144 = 12

12 + 4 = 16

√16 = 4

4 + 32 = 36

√36 = 6

6 + 43 = 49

Given EXPRESSION is,

⇒ 987 + 23% of 1500 = ? + 21% of 700

$(\Rightarrow 987 + \frac{{23}}{{100}} \TIMES 1500 = \;? + \frac{{21}}{{100}} \times 700)$

⇒ 987 + 23 × 15 = ? + 21 × 7

⇒ 987 + 345 = ? + 147

⇒ 1332 = ? + 147

⇒ ? = 1332 – 147 = 1185

⇒ ? = 1185

Follow BODMAS rule to solve this question, as per the order is GIVEN below,

STEP - 1 - Parts of an equation enclosed in 'Brackets' MUST be solved first,

Step - 2 - Any MATHEMATICAL 'Of' or 'Exponent' must be solved next,

Step - 3 - Next, the parts of the equation that contains 'Division' and 'Multiplication' are calculated,

Step - 4 - Last but not least, the parts of the equation that contains 'Addition' and 'Subtraction' should be calculated.

{(32 ÷ 2 + 16 – 4 × 152 ÷ 2) + 34²}

⇒ {(16 + 16 – 4 × 76) + 1156}

⇒ {(16 + 16 – 304) + 1156}

⇒ {(32 – 304) + 1156}

⇒ {(-272) + 1156}

∴ 884

250% of 30 ÷ 300% of 25 = ?% of 100

$(\eqalign{ & Or,\ \ 30 \times \frac{{250}}{{100}} \DIV 25 \times \frac{{300}}{{100}} = 100 \times \frac{?}{{100}} \CR & Or,\ \ 75 \div 75 =\ ? \cr & Or,\ \ ? = 1 \cr})$

Follow these BODMAS rules to solve the question

Step-1? The part of the equation containing 'Brackets' must be solved first, and in the bracket,

Step-2? Any mathematical 'Of' or 'Exponent' must be solved NEXT,

Step-3? Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved

Step-4? At last, the part of the equation that CONTAINS 'Addition' and 'Subtraction' should be solved.

⇒ (1/64)⁰ + (-32)^4/5 + (64)^-1/2 + (32)^2/5 = ?

Anything RAISE to POWER 0 is 1, ∴ (1/64)⁰ is = 1

⇒ ? = 1 + (-2^{5 × 4/5}) + (1/8) + (2^{5 × 2/5})

⇒ ? = 1 + 16 + 1/8 + 4

⇒ ? = 21 + 1/8

Approximating the NUMBERS in the above EXPRESSION:

⇒ (52² – 34²) ÷18 × √? = 1720

⇒ (52 + 34) × (52 – 34)18 × √? = 1720

⇒ (86 × 18) ÷ 18 × √? = 1720

⇒ 86 × √? = 1720

⇒ √? = 1720/86 = 20

Let the MISSING value be ‘x’. According to QUESTION:

⇒ 40% of x = 960

⇒ 40/100 × x = 960

⇒ x = 960 × 100/40

GIVEN expression:

$(\FRAC{1}{8}of\frac{2}{3}\;of\frac{3}{5}\;of\;1715 = ?)$

⇒ ? = (1/8) × (2/3) × (3/5) × 1715

⇒ ? = (1/20) × 1715

⇒ ? = 85.75

$(\left( {1 - \frac{1}{{b - 4}}} \RIGHT)\left( {1 - \frac{1}{{b - 5}}} \right)\left( {1 - \frac{1}{{b - 6}}} \right)\left( {1 - \frac{1}{{b - 7}}} \right) = \frac{{b - 5}}{{b - 4}} \times \frac{{b - 6}}{{b - 5}} \times \frac{{b - 7}}{{b - 6}} \times \frac{{b - 8}}{{b - 7}} = \frac{{b - 8}}{{b - 4}})$

(0.3 × 0.025) + (0.12 × 2.5) – (0.4 × 1.05) = ?

⇒ 0.0075 + 0.3 - 0.42 = ?

⇒ 0.3075 - 0.42 = ?

∴ ? = -0.1125

Follow BODMAS to solve this question, as per the order GIVEN below,

Step-1: Parts of an equation enclosed in ‘Brackets’ must be solved first,

Step-2: Any mathematical ‘Of’ or ‘Exponent’ must be solved next,

Step-3: Next, the parts of the equation that contains ‘Division’ and ‘MULTIPLICATION’ are calculated,

Step-4: LAST but not the least, the parts of the equation that contains ‘Addition’ and Subtraction’ should be calculated.

Given expression,?

2301 ÷ 20.01 × 34.99 + 600.01 = ?

⇒ ? ≈ 2301 ÷ 20 × 35 + 600

⇒ ? ≈ 115 × 35 + 600

⇒ ? ≈ 4625

⇒ 243 = 3^X

⇒ 3 × 3 × 3 × 3 × 3 = 3^x

⇒ 3⁵ = 3^x

LET the VALUE be X

⇒ x = 88% of 1125 + 20% of 425

⇒ x = 1125 × 88/100 + 425 × 20/100

(0.081)^0.14 × (0.081)^0.11 = (0.0081)^{0.14 + 0.11} = (81 × 10^-4)^0.25 = (3⁴ × 10^-4)^25/100 = (3⁴ × 10^-4)^1/4 = 3 × 10^-1 = 0.3

$(\BEGIN{array}{L} \left( {7\frac{3}{5}-3\frac{1}{{15}}} \right) \div 2\frac{7}{{15}} = \left( ? \right)\\ \RIGHTARROW \left( {\frac{{38}}{5}-\frac{{46}}{{15}}} \right) \div \frac{{37}}{{15}} = ? \end{array})$

⇒ ? = (114 – 46)/15 ÷ 37/15

⇒ ? = 68/15 ÷ 37/15

⇒ ? = 68/15 × 15/37

∴ ? = 68/37

⇒ 77.07 + 777.77 + 7.077 + 70.707 – 7.07 = ?

⇒ 854.84 + 77.784 – 7.07 = ?

⇒ ? = 932.624 - 7.07

∴ ? = 925.554

$({\left( { - 7776} \right)^{\FRAC{2}{5}}} = {\left[ {\left( { - {2^5}) \times ( - {3^5}} \right)} \right]^{\frac{2}{5}}})$

$( \Rightarrow {\left( { - 2} \right)^{5 \times \frac{2}{5}}} \times {\left( { - 3} \right)^{5\; \times \;\frac{2}{5}}})$

$( \Rightarrow {\left( { - 2} \right)^{2\;}} \times {\left( { - 3} \right)^{2\;}} = 4 \times 9 = 36)$

$(\SQRT[3]{{729}} \TIMES \sqrt {16}+ \sqrt {676}+ \sqrt {169})$

⇒ 9 × 4 + 26 + 13

⇒ 36 + 26 + 13

⇒ 75

FOLLOW BODMAS rule to solve this question, as per the order given below,

Step-1: Parts of an equation ENCLOSED in the ‘BRACKETS’ must be solved first

Step-2: Any mathematical ‘OF’ or ‘EXPONEMTS’ must be solved next

Step-3: Next the PART of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step-4: Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

⇒ ?² + √1024 = 561

⇒ ?² + 32 = 561

⇒ ?² = 561 – 32

⇒ ?² = 529

⇒ ?² = (23)²

0.6% = 0.6/100 = 0.006

We can WRITE following values as :

84.90 ≈ 85, 110.40 ≈ 110 and 70.30 ≈ 70

337.40 ≈ 337 and 52.75 ≈ 53

Given EXPRESSION is,

⇒ 84.90 + 110.40 – 70.30 = 337.40 – 52.75 × ?

⇒ 85 + 110 – 70 = 337 – 53 × ?

⇒ 195 – 70 = 337 – 53 × ?

⇒ 125 = 337 – 53 × ?

⇒ 337 – 125 = 53 × ?

⇒ 212 = 53 × ?

⇒ ? = 212/53

31.992 × 28.196/6.932 + 677.993 – 320.898 = ? × 4.889

Taking their APPROX. values

⇒ 32 × 28/7 + 678 – 321 = ? × 5

⇒ 32 × 4 + 678 – 321 = ? × 5

⇒ ? × 5 = 128 + 678 – 321

⇒ ? = 485/5

⇒ ? = 97

GIVEN that,

{[√(X^-3/5)]^-5/3}⁵

⇒ (x^-3/5)^{1/2 × (-5/3) × 5}

⇒ (x^-3/5)^-25/6

⇒ (x)^{-25/6 ×-3/5} = x^5/2

Given, 4/7 of the birthday CAKE was eaten on your birthday

Fraction of cake LEFT = 1 – 4/7 = 3/7

Now, next day your dad ate 1/2 of what was left

$({\rm{Fraction\;of\;cake\;left}} = \frac{3}{7} - \frac{1}{2} \times \frac{3}{7} = \frac{3}{{14}})$

51.97 - (81.18 - X) - 59.39 = 5.628

⇒ 51.97 - 81.18 + x - 59.39 = 5.628

⇒ x - 29.21 - 59.39 = 5.628

⇒ x = 5.628 + 29.21 + 59.39