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Let the amount donated by John = ₹x 

The amount donated by Ismail is ₹85 more than twice of John. 

So, the amount donated by Ismail = ₹(2x + 85) 

Total amount = John amount + Ismail amount = ₹4000 

⇒ x + 2x + 85 = 4000 

⇒ 3x + 85 = 4000 

⇒ 3x + 85 – 85 = 4000 – 85 (Subtract 85 on both sides) 

⇒ 3x = 3915

⇒ 3x/3 = 3915/3 (Divide by 3 on both sides) 

⇒ x = 1305 

∴ Money donated by John = x = ₹ 1305 

∴ Money donated by Ismail = 2x + 85 

= 2(1305) + 85 

= ₹2695

Let the number = x 

Consecutive number of x = x + 1 

Given that, x + (x + 1) = 125 

⇒ 2x + 1 = 125 

⇒ 2x = 125 – 1 

⇒ 2x = 124

⇒ x = 124/2

x = 62 and x + 1 = 62 + 1 = 63 

∴ Required numbers are 62 and 63. 

Check: 

Numbers: 62, 63 

Sum = 62 + 63 = 125 

Hence verified.

Correct option is C) 9

Given 25 = 18 – 7(b – 6) 

⇒ 25 – 18 = l8 – 7(b – 6) – 18 (Subtract 18 on both sides) 

⇒ 7 = – 7(b – 6) 

⇒ \(\frac {7}{-7} = \frac {-7(b-6)}{-7}\)(Divide by – 7 on both sides) 

⇒ – 1 = b – 6 

⇒ – 1 + 6 = b – 6 + 6 (Add 6 on both sides) 

⇒ 5 = b 

∴ b = 5 (By transposition) 

Check: 

Substitute b = 5 in the given equation. 

RHS = 18- 7(b – 6) – = 18-7(5-6) 

= 18 – 7(- 1) 

= 18 + 7 = 25 = LHS 

Hence verified.

Correct option is B) 4

2x + 5 = 13

⇒ 2x = 13 - 5 = 8

⇒ x = 8/2 = 4

Correct option is C) 2(x – 3)

(B) \(\frac{k-5}2\)

 2x + 5 = k

⇒ 2x = k - 5

⇒ x = \(\frac{k-5}2\)

Correct option is A) y – 5

Correct option is B) 4x – 5

(i) A number m is decreased by 5 is 12.

(ii) One third of a is 4.

(iii) Sum of 4 times of x and 7 is 15. (or) 7 is added to 4 times of x is 15.

(iv) 2 is decreased by 3 times of y is 11. (or) 3 times of y is subtracted from 2 is 11.

Correct option is A) 1

y = -2 then 3 + y = 3 + (-2)

= 3 - 2 = 1

Correct option is C) -45/11

-9/z = -11/5

⇒ z = -9 x 5/-11 = \(\frac{5}{-11}=\frac{9\times5}{11} = \frac{45}{11}\) 

\(\therefore\) -(z) = \(-\frac{45}{11}\)

Correct option is D) 8

198 = 25z - 2

⇒ 25z = 198 +2 = 200

⇒ z = 200/25 = 8

Correct option is B) – 1

4x - 3 = 3x - 4

⇒ 4x - 3x = 3 - 4

⇒ x = -1

Correct option is A) – 2

3(x - 3) = 5(2x + 1)

⇒ 3x - 9 = 10x + 5

⇒ 10x - 3x = -9 - 5

⇒ 7x = -14

⇒ x = -14/7 = -2

Correct option is D) 36°

Correct option is B) 8cm

Correct option is C) 1

7x - 111 = 7 - 11x

⇒ 7x + 11x = 7 + 11

⇒ 18x = 18

⇒ x = 18/18 = 1

D) 7 + x

A number x is increased by 7 is represented as x + 7.

Correct option is B) 16 – p

Correct option is D) –

C) 15

Let the number be x.

\(\therefore\) According to given condition, we have

2x - 3 = 27

⇒ 2x = 27 + 3 = 30

⇒ x = 30/2 = 15

Correct option is A) 15 + y

Correct option is C) multiplies

Let the first number = x 

Then the second number = x + 7 (exceeds first number by 7) 

Sum of two numbers = 35 According to problem, x + x + 7 = 35 

⇒ 2x + 7 = 35 

⇒ 2x = 35 – 7

 ⇒ 2x = 28

⇒ x = 28/2

⇒ x = 14 x + 7 

= 14 + 7 = 21 

∴ The two numbers are 14 and 21

Check: 

Numbers: 14, 21 

Sum = 14 + 21 = 35 

Hence verified

Correct option is B) 11 + x

B) 3x = 22

Let the number be x.

\(\therefore\) According to given condition.

3x - 2 = 20

⇒ 3x = 20 + 2 = 22

D) 29 – x

Let the other number by y.

Then x + y = 29

⇒ y = 29 - x

i.e., other number be x 29 - x

3k + 4 = 28 

⇒ 3k + 4 – 4 = 28 – 4 (Add both sides ‘- 4’) 

⇒ 3k = 24

⇒ 3k/3 = 24/4 (Divide both sides by ‘3’)

⇒ k = 8

Check: 

Substitute k = 8 in the given equation. 

LHS = 3k + 4 

= 3(8) + 4 

= 24 + 4 = 28 = RHS 

Hence verified.

– 4(x – 1) = 16 

⇒ 4x + 4 = 16 (Distributive property) 

⇒ – 4x + 4 – 4 = 16 – 4 (Subtract both sides ‘4’) 

⇒ – 4x = 12 

⇒ (- 4x) × (- 1) = 12 × (- 1) (Multiply with ‘- 1 ‘on both sides) 

⇒ 4x = – 12

⇒ 4x/4 = -12/4 (Divide both sides by ‘4’) 

⇒ x = – 3 

Check: 

Substitute x = – 3 in the given equation. 

LHS = – 4(x – 1) 

= – 4(- 3 – 1) 

= – 4 (- 4) = 16 

= RHS 

Hence verified. 

5(x + 1) – 2(x – 7) = 13 

⇒ 5x + 5 – 2x + 14 = 13 (distributive law) 

⇒ (5x – 2x) + (5 + 14) = 13 (regrouping like terms) 

⇒ 3x +19 = 13 

⇒ 3x = 13 – 19 (∵ +19 transposed arid becomes)

⇒ 3x = – 6

⇒ x = -6/3 (∵ × 3 transposed and becomes ÷ 3) 

⇒ x = – 2

2(b + 3) + 13 = 27 

⇒ 2b + 6 + 13 = 27 (distributive law) 

⇒ 2b + 19 = 27 

⇒ 2b = 27 – 19 (∵+ 19 transposed and becomes – 19) 

⇒ 2b = 8 

⇒ b = 8/2 (∵ × 2 transposed and becomes ÷ 2) 

⇒ b = 4 

Check: 

Substitute b = 4 

LHS = 2(b + 3) + 13 

= 2(4 + 3) + 13 

= 2(7) + 13 

= 14 + 13 

= 27 = RHS 

Hence verified.

13 is taking away from 3 times of m is 25.

Two times (twice) a number is 15.

From the above figure, 

Side of square = (3x – 5) m 

Perimeter of square = 40 m

⇒4 × side = 40 ⇒ 4 × (3x – 5) = 40

⇒ \(\frac {4(3x-5)}{4} = \frac {40}{4}\) (Divide by 4 on both sides) 

⇒ 3x – 5 = 10 

⇒ 3x – 5 + 5 = 10 + 5 (Add 5 on both sides) 

⇒ 3x = 15

⇒ 3x/3 = 15/3 (Divide by 3 on both sides)

∴ x = 5 m

Let largest number = 3x and smallest

number = 2x 

Difference = 3x – 2x = x 

But as per the problem difference = 5 

⇒ x = 5 

∴ Largest number = 3x = 3 × 5 = 15

Perimeter of a triangle = 15 cm 

Perimeter = x + x + 2 + 2x – 3 = 4x – 1 

∴ 4x – 1 = 15 

⇒ 4x = 15 + 1

⇒ 4x = 16 

⇒ x = 4

One fourth of n is 5.

x + x + x = 5 + 5 + 1 + 1 

3x = 12

Straight angle = 180° 

∠ AOB = 180° 

∠ AOB + ∠ BOD = 180° 

x + 30° + x = 180° 

⇒ 2x + 30° = 180° 

⇒ 2x + 30° – 30° – 180°- 30° (Subtract 30° on both sides) 

⇒ 2x = 150°

⇒ 2x/2 = 150°/2 (Divide by 2 on both sides)

∴ x = 75°

Consider an equation 7x = 14 

If we multiply by two different numbers 5 and 8 on either side. 

7x × 5 = 14 × 8 

⇒ 35x = 112 

So, the equation 7x = 14 is not equal to 35x = 112

Let the width of a rectangle (b) = x m 

Then the length of a rectangle (l) 

= 20 more than its width 

= (x + 20) m 

Perimeter of the rectangle = 100 m 

⇒ 2(1 + b) = 100 

⇒ 2(x + 20 + x) = 100 

⇒ 2(2x + 20) = 100 

⇒ 4x + 40 = 100 

⇒ 4x + 40 – 40 = 100 – 40 (Subtract 40 on both sides) 

⇒ 4x = 60 4x 60

⇒ 4x/4 = 60/2 (Divide by 4 on both sides) 

⇒ x = 15 m 

∴ Width x = 15 m 

Length = x + 20 = 15 + 20 = 35 m

Let the quantity of wheat consumed in the month x kg. 

Quantity of rice = 4 times of wheat = 4x kg 

Quantity of rice + Quantity of wheat = 30 kg 

⇒ 4x + x = 30 

⇒ 5x = 30

⇒ 5x/5 = 30/5 (Divide by 5 on both sides) 

⇒ x = 6 kg 

∴ Quantity of wheat = 6 kg 

Quantity of rice = 4x = 4 × 6 = 24 kg

Correct option is A) 2p

4 is added to a number is 9.

Given number = m 

By adding 1/3 to m = m + 1/3 

then, m + 1/3 = 25.

Given angles are x, x + 20 

Sum of angles = x + x + 20 

Sum of angles is straight angle (180°).

⇒ x + x + 20 = 180° 

∴ 2x + 20 = 180°

Let width of rectangle = x 

Length of rectangle 

= 2 more than width = x + 2 

Perimeter = 2 (length + width) 

= 2(x + 2 + x) = 2(2x + 2) 

Given Perimeter = 16 cm 

∴ 4x + 4 = 16

Taking away 7 from ‘y’ is 11.

Let the number = n 

3 times the number = 3n 

By adding 7 the result = 3n + 7 

∴ 3n + 7 = 13