BANK & INSURANCE (RATIO AND PROPORTION) PART 2

Let ‘x’ be the number of months for which Mahesh invested his Rs.111.

555×12x×111=151\frac{555 × 12}{x × 111} = \frac{15}{1}x×111555×12​=115​ 60x=15\frac{60}{x} = 15x60​=15

⇒ x = 4

⇒ Mahesh invested his money for 4 months, i.e. 12 − 4

= 8 months after Manoj invested his money

∴ Mahesh joined after 8 months.

Let Ashish purchased x kg of rice

So, quantity of wheat he purchased = (50 − x)

Now,

x × 12 + (50 − x) × 17 = 710

12x + 850 − 17x = 710

5x = 140

⇒ x = 28 kg

∴ Money spent on rice = 12 × 28 = Rs. 336

Let the price of P per kg = Rs. 3x and the price of Q per kg = Rs. 2x

⇒ Price of 1 kg of R = 3/8 × 3x + 5/8 × 2x

= 19x/8

According to the question,

6.70 − 2.90 = 19x/8

⇒ 3.80 × 8 = 19x

⇒ x = Rs. 1.6

∴ Cost of Q per kg = Rs. 1.6 × 2 = Rs. 3.2

The amount left with A after shopping = 350 × 2/7 = Rs. 100

The amount left with B after shopping

= 350 − 100

= Rs. 250

 Let amount spent on shopping by A and B each be Rs. m

⇒ 10a − 100 = m
⇒ 13a − 250 = m

Then,

⇒ 10a − 100 = 13a − 250

⇒ a = 50

∴ The amount spent by A on shopping = 500 − 100 = Rs. 400

40 liters of a 50% alcohol solution will contain:

Water = 20 liters
Alcohol = 20 liters

Let x liters of 75% alcohol solution is mixed with the above solution.

The 75% alcohol solution will contain:

Alcohol = 75/100 × x = 3x/4 liters

Water = x − 3x/4 = x/4 liters

New volume of mixture = (40 + x) liters

New volume of alcohol = (20 + 3x/4) liters

New volume of water = (20 + x/4) liters

∴ New concentration =

20+3x/440+x×100\frac{20 + 3x/4}{40 + x} × 10040+x20+3x/4​×100 60=80+3x40+x×10060 = \frac{80 + 3x}{40 + x} × 10060=40+x80+3x​×100

⇒ 0.6 × 4(40 + x) = 80 + 3x

⇒ 96 + 2.4x = 80 + 3x

⇒ 0.6x = 16

∴ x = 16/0.6 = 80/3 = 26.67 liters

First of all, we use given quantities and place them in the formula, to know the required quantities.

Cost of 1 kg rice of first type = Cost price of dearer = d = Rs. 11.80

Cost of 1 kg rice of second type = Cost price of cheaper = c = Rs. 9.40

Desired cost of 1 kg of the mixture = Mean price = m = Rs. 10

Required rate = Quantity of cheaper/Quantity of Dearer

=d−m / m−c

=>Quantity of cheaper/Quantity of Dearer= 11.80−10 / 10−9.40 = 1.80 / 0.60 

= 3 : 1

∴ The ratio of the mixture should be 3 : 1

A : B = 4 : 5

B : C = 3 : 2

Difference between the lengths of A and C is 8 cm

Let the lengths of A and B be 4x cm and 5x cm respectively.

Ratio of lengths of B and C = 3 : 2

⇒ 5x / Length of C = 3/2

⇒ Length of C = 2/3 × 5x = 10x/3 cm

Now,

Difference between lengths of A and C = 8 cm

⇒ 4x − 10x/3 = 8

⇒ 12x − 10x = 24

⇒ x = 24/2 = 12 cm

∴ Length of metal rod =

4x + 5x + 10x/3

= 4(12) + 5(12) + (10/3 × 12)

= 48 + 60 + 40 = 148 cm

1945 chocolates have to be divided between 12 men, 11 women and 8 children in the ratio 11 : 11 : 17.

∴ Compounded ratio is (12×11) : (11×11) : (8×17)

⇒ 132 : 121 : 136

The share of men = [132 / (132+121+136) ]×1945

= 132 × 5 = 660

Ratio of amount invested in share market and gold is 6 : 7

Profit earned on the investment after one year is 30%

Ratio of amount reinvested in share market and gold is 4 : 5

Amount reinvested in gold is Rs. 94,500

Since the amount reinvested is in the ratio 4 : 5

Then total amount reinvested,

⇒ (Amount of gold reinvested × total of ratio)/part of gold in ratio

⇒ (94,500 × 9)/5 = Rs. 1,70,100

Since there was a profit in this amount = 30%

So the Original amount,

⇒ (Total amount reinvested × 100)/130

= Rs. 130846

Original amount invested in gold,

⇒ (130846 × 7)/13

= Rs. 70,455.53 ≈ Rs. 70,456

∴ Original amount invested in gold is Rs. 70,456

Old Ratio = 2 : 3 : 4

New Ratio = 7 : 2 : 5

Now,

2 + 3 + 4 = 9 and 7 + 2 + 5 = 14

We will have to make both the ratios equal, So multiplying 1st ratio by 14 and 2nd by 9 we get

Old Ratio = 2 × 14 : 3 × 14 : 4 × 14

= 28 : 42 : 56

New Ratio = 7 × 9 : 2 × 9 : 5 × 9

= 63 : 18 : 45

Sum will be 126

Earlier Sita gets 42 units and now 18 units

Difference = 42 − 18 = 24 units (which is given as Rs.60 in the question)

24 units = 60

1 unit = 60/24 = 2.5

126 units = Rs. 315