Question

Sujatha spends x% of her income. If her income increases by 14% and the expenditure increases by 10%, her savings increase by 22%. What is the value of x?​

Answer 1

Step-by-step explanation:

Given: Rishu saves x% of her income

Increase in her income = 26%

Increase in her expenditure = 20%

Increase in saving = 50%

Concept used: Income = Saving + Expenditure

Calculations: Let income of Rishu be 100 Saving of Rishu = 100 × (x/100) = x

Expenditure of Rishu = 100 – x

Rishu's salary after increment = 100 × (126/100) = 126

Rishu's expenditure after increment = (100 – x) × 120/100 = (100 – x) × 6/5

New Saving = 126 – (100 – x) × 6/5 ----(1)

New saving after increment = x × 150/100

New saving after increment = 3x/2 ----(2)

From eq. (1) and eq. (2)

⇒ 126 – (100 – x) × 6/5 = 3x/2

⇒ 126 – 120 + 6x/5 = 3x/2

⇒ 6 = (3x/2) – (6x/5)

⇒ 6 = (15x – 12x)/10

⇒ x = 20 ∴ The value of x is 20

Answer 2

Solution :-

Let us assume that, the total income is Rs. 100y .

So,

→ Sujatha spends = x% of 100y = (x * 100y)/100 = Rs. xy

then,

→ Saving = Total Income - Expenditure

→ Saving = (100y - xy) = Rs. y(100 - x)

now,

→ New income = 114% of 100y = (114 * 100y)/100 = Rs. 114y

→ New expenditure = 110% of xy = Rs. 1.1xy

then,

→ New saving = (114y - 1.1xy) = Rs. y(114 - 1.1x)

A/q,

→ New saving = 122% of previous saving

→ y(114 - 1.1x) = 1.22y(100 - x)

→ 114 - 1.1x = 122 - 1.22x

→ 1.22x - 1.1x = 122 - 114

→ 0.12x = 8

→ x = 66.67% (Ans.)

Hence, value of x is equal to 66.67% .

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