Question

After 12 years, Manoj will be 3 times as old as he was 4 years ago. Find his present age

2. The age of sonal and manoj are in the ratio 7:5. Ten years hence their ratio will ne 9:7.

Find their present ages.

3. ⅔ of a number is greater than ⅓ by 3. Find the number

4. If the cost of 3 table and 2 chair is Rs. 1850. If a table costs Rs. 75 more than the chair,

find the price of each

5. A number when multiplied by 4 exceeds itself by 45. Find the number.​

Answer 1

AnswEr – 1 :

Let the Manoj's present age be x years.

ATQ,

• After 12 years, Manoj will be 3 times as old as he was 4 years ago.

After 12 years,

• His age = (x + 12)

Before 4 years,

• His age = (x – 4)

$\dashrightarrow\sf x + 12 = 3\Big\{x - 4\Big\} \\\\\\\dashrightarrow\sf x + 12 = 3x - 12\\\\\\\dashrightarrow\sf - 2x = - 12 - 12\\\\\\\dashrightarrow\sf -2x = -24\\\\\\\dashrightarrow\sf x = \cancel\dfrac{-24}{-2}\\\\\\\dashrightarrow{\pmb{\sf{x = 12}}}$

⠀⠀⠀⠀

∴ Present age of Manoj is 12 years.

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AnswEr – 2 :

Let the present age of Sonal and Manoj be 7x and 5x respectively.

Ten years hence,

• Sonal's age = (7x + 10)
• Manoj's age = (5x + 10)

⇥ 7x + 10 + 5x + 10 = 9x + 7x

⇥ 9x – 5x = 20

⇥ 4x = 20

⇥ x = 20/4

⇥ x = 5

∴ Hence, present age of Sonal and Manoj is 35 and 25 years.

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AnswEr – 3 :

Let the number be n.

• ⅔ of a number is greater than ⅓ by 3.

$\dashrightarrow\sf \dfrac{2}{3}n = \dfrac{1}{3}n + 3 \\\\\\\dashrightarrow\sf \dfrac{2}{3}n - \dfrac{1}{3}n = 3\\\\\\\dashrightarrow\sf \dfrac{n}{3} = 3\\\\\\\dashrightarrow{\pmb{\sf{n = 9}}}$

∴ Hence, the number is 9.

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AnswEr – 4 :

Let x be the cost of chair. Then, table's cost be (x + 75)

A/Q,

• The cost of 3 table and 2 chair is Rs. 1850.

⇥ 3(x + 75) + 2x = 1850

⇥ 3x + 225 + 2x = 1850

⇥ 5x = 1850 – 225

⇥ 5x = 1625

⇥ x = 1625/5

⇥ x = 325

∴ Hence, the cost of chair is 325 rs and cost of table is 400 rs.

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AnswEr – 5 :

Let the number be n.

⇥ 4n = n + 45

⇥ 4n – n = 45

⇥ 3n = 45

⇥ n = 45/3

⇥ n = 15.

∴ Hence, the number is 15.

Answer 2

1]

Given :-

After 12 years, Manoj will be 3 times as old as he was 4 years ago.

To Find :-

Present ages

Solution :-

Let the age of Manoj be M

Given,

After 12 years, Manoj will be 3 times as old as he was 4 years ago

M + 12 = 3 × (M - 4)

M + 12 = 3M - 12

3M - M = 12 + 12

2M = 24

M = 24/2

M = 12

2]

Given :-

The age of sonal and manoj are in the ratio 7:5. Ten years hence their ratio will ne 9:7

To Find :-

Present age

Solution :-

Let the ages be 7y and 5y

7y + 10/5y + 10 = 9/7

7(7y + 10) = 9(5y + 10)

49y + 70 = 45y + 90

49y - 45y = 90 - 70

4y = 20

y = 20/4

y = 5

Age of Sonal = 7(5) = 35 years

Age of Manoj = 5(5) = 25 years

3]

Given :-

⅔ of a number is greater than ⅓ by 3. Find the number

To Find :-

Number

Solution :-

Let the number be a

2a/3 = a/3 + 3

2a - a/3 = 3

a/3 = 3

a = 3 × 3

a = 9

Given :-

If he cost of 3 table and 2 chair is Rs. 1850. If a table costs Rs. 75 more than the chair,

To Find :-

Price of each

Solution :-

Let the cost of table be x and cost of chair be y

x = y + 75

3x + 2y = 1850

Table cost Rs. 75 more than chair

3(y + 75) + 2y = 1850

3y + 225 + 2y = 1850

3y + 2y = 1850 - 225

5y = 1625

y = 1625/5

y = 325

Cost of table = 325 + 75 = Rs. 400

5]

Given :-

A number when multiplied by 4 exceeds itself by 45.

To Find :-

Number

Solution :-

Let the number be a

4 × a = a + 45

4a = a + 45

4a - a = 45

3a = 45

a = 45/3

a = 15

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