model 11 ratio & partnership Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

B entered after x months.

Ratio of equivalent capitals for 1 month

= 64000 × 12 : 48000 (12 - x)

= 16 : (12 - x)

$16/{12 - x} =2/1$ ⇒ 24 - 2x = 16

2x = 8 ⇒ x = 4 months

Answer: (d)

Let x kg of sugar costing Rs.20/ kg and y kg of sugar costing Rs.15/kg are mixed.

According to the question,

20x + 15y = 16 (x + y)

20x + 15y = 16x + 16y

20x - 16x = 16y - 15y

4x = y ∴ $x/y = 1/4$ or 1 : 4

Method 2 :

By the rule of alligation,

∴ Required ratio = 1 : 4

Answer: (b)

According to the question

$\text"Cost price"/ \text"Selling price" = 5/4$

Selling price = $4/5$ × Cost price

Loss = Cost price - Selling price

= Cost price - $4/5$ Cost price = $1/5$ Cost price

Loss % = ${{1/5}\text"Cost price" × 100}/\text"Cost price" = 100/5 = 20%$

Method 2 : Simple Approach

Rs.1 is loss on Rs.5.

loss % = $1/5$ × 100 = 20%

Here, C.P. = 5x, S.P. = 4x

Loss% = $\text"Loss"/ \text"C.P."$ × 100

= ${5x - 4x}/{5x}$ × 100 = 20%

Answer: (b)

Let Milk : Water = K : 1

S.P. = (K + 1) × 9

C.P. = 10K; Gain = 9 - K

Gain % = ${9 - K}/{10K} × 100$

${9 - K}/{10K} × 100$ = 20

90 - 10K = 20K

30K = 90 ⇒ K = 3

Ratio = 3 : 1

Answer: (b)

Ratio of profit sharing among A, B and C

= Ratio of equivalent capitals of

A, B and C for 1 month

= 320000 × 4 : 510000 × 3 : 270000 × 5

= 32 × 4 : 51 × 3 : 27 × 5

= 128 : 153 : 135

Sum of ratios = 128 + 153 + 135 = 416

Total profit = Rs.124800

A’s share = $128/416 × 124800$ = Rs.38400

Answer: (d)

C.P. of 40kg of mixture

= Rs.(15 × 29 + 25 × 20)

= Rs.(435 + 500) = Rs.935

S.P. of 40kg of mixture

= 27 × 40 = Rs.1080

Gain = 1080 - 935 = Rs.145