model 11 percentage with ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Let the numbers be x and y where x > y.

Then, x - y =$15/100$(x + y)

x – y = $3/20$(x + y)

20x – 20y = 3x + 3y

20x – 3x = 20y + 3y

17x = 23y ⇒ $x/y = 23/17$

Answer: (c)

$(B – A) × 30/100 = (B + A) × 18/100$

${B - A}/{B + A} = 18/30 = 3/5$

By componendo and dividendo,

${2B}/{- 2A} = {3 + 5}/{3 - 5} = 8/{-2} = 4/{-1}$

$B/A = 4/1$ = A : B = 1 : 4

Answer: (b)

Let the numbers be 4x and 5x.

After corresponding increase or decrease,

Required ratio = ${4x} × 120/100 : {5x} × 80/100$

= 12x : 10x = 6 : 5

Answer: (d)

10% of m = 20% of n

$10/100 × m = 20/100 × n$

$m/n = 10/5 = 2/1$

m : n = 2 : 1

Answer: (d)

Percentage of syrup = $3/4$ × 100 = 75%

Answer: (b)

Let the initial expenses on rice, fish and oil be Rs.12x, Rs.17x and Rs.3x respectively.

Total expenditure = Rs.(12x + 17x + 3x) = Rs.32 x

After increase,

Expenditure on rice = $120/100 ×12x = Rs.14.4x$

Expenditure on fish = $130/100 × 17x = Rs.22.1x$

Expenditure on oil = $150/100 × 3x = Rs.4.5x$

Total expenditure =Rs.(14.4 x + 22.1x + 4.5 x) =Rs.41 x

Increase = Rs.(41x – 32x) = Rs.9x

Percentage increase =${9x}/{32x} × 100 =225/8 = 28{1}/8$%