AAO Exam-CT 5: Quant (Ratio and Proportion)

AAO Exam-CT 5- Quant (Ratio and Proportion)

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AAO Exam-CT 5: Quant (Ratio and Proportion)

1. The price of toys A, B, C are in the ratio 4 : 5 : 3 If the increments of 10%, 6% and 20% are allowed respectively in their prices, then what will be new ratio of their prices?

  • 44 : 53 : 36
  • 53 : 44 : 36
  • 36 : 55 : 44
  • Can't be determined 
  • None of these

Given:

Price of toys A, B, C are in the ratio 4 : 5 : 3

Increments of 10%, 6% and 20% are allowed respectively in their prices

Calculations:

Let A = 4x, B = 5x and C = 3x.

New price of toy A = (110/100) ​of 4x = (110/100) ​× 4x = (44/10)x​

New price of toy B = (106/100)​ of 5x= (106/100) × 5x = (53/10)x​

New price of toy C = (120/100)​ of 3x = (120/100​) × 3x = (36/10)x

⇒ New ratio (A : B : C) = (44/10)x ​: (53/10)x : (36/10)x = 44 : 53 : 36

 New ratio of their prices is 44 : 53 : 36

2. Three types of sugar are mixed together. Their volumes are in the ratio 3 : 5 : 7 and the weight of equal volumes is in the ratio 4 : 2 : 3. What is the weight of the sugar of the first type if the weight of the mixture is 387 kg?
  • 120 kg
  • 108 kg
  • 132 kg
  • 96 kg
  • 144 kg

Given:

Volume ratio = 3 : 5 : 7

Weight ratio of equal volume = 4 : 2 : 3

Total mixture = 387 kg

Calculation:

Weight ratio = (3 × 4) : (5 × 2) : (7 × 3)

⇒ 12 : 10 : 21

Total weight = 43 ratio

Required weight = 387/43 × 12 = 108 kg

∴ The answer is 108 kg

3. The income of A and B are in the ratio 9 : 11 and their expenditure is in the ratio 5 : 7. If each of them saves Rs. 4400, then find the difference of their incomes. 
  • Rs. 1100
  • Rs. 2200
  • Rs. 3300
  • Rs. 4400
  • Rs. 3500

Given:

Income = 9 : 11

Expenditure = 5 : 7

savings = Rs. 4400

Calculation:

Let the income of A be Rs. 9x

Income of B = Rs. 11x

Expenditure of A = 5y

Expenditure of B = 7y

So, 9x - 5y = 4400      ----(1)

11x - 7y = 4400      ----(2)

(1) × 7 - (2) × 5 gives,

63x - 35 y - 55x + 35y = 8800

⇒ 8x = 8800

⇒ x = Rs. 1100 

∴ Difference = 2x = Rs. 2200

∴ The answer is Rs. 2200

  

Savings = 9 - 5 = 4 ratio, 11 - 7 = 4 ratio

A.T.Q

4 ratio = 4400

Difference = 2 ratio = Rs. 2200

∴ The answer is Rs. 2200

4. A and B are two alloys of silver and zinc in the ratio 2 : 3  and 5 : 2. Equal quantities of these alloy are mixed to form a new alloy. Find the ratio silver and zinc in the new alloy.

  • 39 : 31
  • 20 : 16
  • 12 : 21
  • 16 : 20
  • 31 : 39

Given:

Ratio of silver and zinc in A = 2 : 3

Ratio of silver and zinc in B = 5 : 2

Calculation:

Silver in A = 2/5

Zinc in A = 3/5

Silver in B = 5/7

Zinc in B = 2/7

Ratio of silver and zinc in the new mixture = (2/5 + 5/7)/(3/5 + 2/7)

⇒ 39/35 : 31/35

New ratio = 39 : 31

∴ Ratio of Silver and Zinc in new alloy = 39 : 31.

5. Nine tickets to Delhi and two tickets to Amritsar cost as much as two tickets to Delhi and seven tickets to Amritsar. What is the ratio of the cost of a ticket to Delhi that of Amritsar?

  • 7 :5
  • 4 :7
  • 5 :7
  • 3 :1
  • 7 :9

Given:

Price of nine tickets to Delhi and two tickets to Amritsar = Price of two tickets to Delhi and seven tickets to Amritsar

Calculation :

Let the cost of a ticket to Delhi be Rs. x and of Amritsar be Rs. y.

⇒ Cost of nine tickets to Delhi and two tickets to Amritsar is = 9x + 2y

⇒ Cost of two tickets to Delhi and seven tickets to Amritsar is = 2x + 7y

⇒ 9x + 2y = 2x + 7y

⇒ 7x = 5y

⇒ x/y = 5/7

Hence the ratio of the cost of a ticket to Delhi that is Amritsar is 5 : 7.

6. In a bag, there are Rs. 5 and Rs. 10 coins in the ratio of 4 : 11 respectively. The difference between the amount of Rs.10 coins and Rs. 5 coins is Rs. 180. Find the average number of coins in the bag.
  • 12
  • 15
  • 10
  • 18
  • 16

Given:

In a bag, there are Rs.5 and Rs.10 coins in the ratio of 4 : 11 respectively. The

difference between the amount of Rs.10 coins and Rs.5 coins is Rs.180

Calculation:

Let number of Rs.5 and Rs.10 coins be 4a and 11a respectively.

The amount of Rs.5 coins = 5 × 4a = Rs.20a

The amount of Rs.10 coins = 10 × 11a = Rs.110a

⇒ 110a - 20a = 180

⇒ a = 2

Total number of coins in a bag = 4a + 11a = 15a = 15 × 2 = 30

Required average = 30/2 = 15

∴ the correct answer is 15.

7. The four numbers are in ratio 8 : 7 : 5 : 13. The difference between the largest and smallest number is 4800. What is the value of the smallest number?

  • 2000
  • 3000
  • 5000
  • 6000
  • 7000

Given:

The ratio of the four numbers is 8 : 7 : 5 : 13

Calculation:

Let the numbers be 8x, 7x, 5x and 13x

13x – 5x = 4800

⇒ 8x = 4800

⇒ x = 600

⇒ Smallest number = 5x

⇒ 5 × 600 = 3000

 The smallest number is 3000.

8. The ratio of Ram’s Salary for May 2020 to his salary for June 2020 was 4 : 3 and the ratio of the salary of June 2020 to October 2020 were 6 : 9. Ram got Rs. 8,000 more salary in October from May 2020, and receives 10% of the salary as Diwali Bonus in October, Find the amount of bonus.

  • Rs.7,000
  • Rs.7,200
  • Rs.7,400
  • Rs.7,240
  • None of these

Given:

Ratio of Ram’s Salary for May 2020 to his salary for June 2020 = 4 : 3

Ratio of Ram’s Salary for June 2020 to October 2020 = 6 : 9

Concept:

If A is x% of B

Than, x% = (A/B) × 100

Calculation:

Salary in May : Salary in June : Salary in October = 4 × 6 : 6 × 3 : 9 × 3

⇒ 24 : 18 : 27

Or 8x : 6x : 9x

Ram got Rs.8,000 more salary in October from May 2020 = 9x – 8x

⇒ x = 8000

Diwali Bonus amount in October = 10% of (9 × 8000)

⇒ Rs.7,200

 Amount of bonus is Rs. 7,200

9. An amount of sum is to be divided between A, B and C in the ratio of 1 : 3 : 4 in this month and the difference between B and C’s share is Rs. 1600. If the total amount becomes twice the next month, find the total amount of the sum in the next month.

  • Rs. 24800
  • Rs. 32000
  • Rs. 28800
  • Rs. 25600
  • Rs. 22400

Given:

Ratio of A, B and C in this month for the sum divided = 1 : 3 : 4

Difference between B's share and C's share = Rs. 1600

Amount becomes twice the next month.

Calculation:

Let the amount to be divided between A, b and C be x, 3x and 4x

Total amount in this month = x + 3x + 4x = 8x 

According to the question,

⇒ 4x – 3x = 1600

⇒ x = 1600

Total amount this month = 8 × 1600 = Rs. 12,800

Total amount for next month = Rs. 12,800 × 2

⇒ Rs. 25,600

∴ The total amount for next month is Rs. 25,600

10. The number of Rs. 5 coins is 15 more than Rs. 10 coins in a wallet. The number of coins of Rs. 5 is 37.5% more than the number of coins of Rs. 10. Find the ratio of the total amount of Rs. 10 coins and Rs. 5 coins.
  • 4 : 7
  • 16 : 11
  • 4 : 11
  • 16 : 9
  • 4 : 9

GIVEN :

The number of Rs. 5 coins is 15 more than Rs. 10 coins in a wallet.

The number of coins of Rs. 5 is 37.5% more than the number of coins of Rs. 10.

FORMULA USED :

X% of Y = XY/100

ASSUMPTION :

Let the number of Rs. 10 and Rs. 5 coins be A and (A + 15) respectively.

CALCULATION :

⇒ A + 15 = A × 137.5/100

⇒ A = 40

Number of Rs. 5 coins = 40 + 15 = 55

Number of Rs. 10 coins = 40

Ratio between the number of Rs.10 and Rs.5 coins = 40 : 55 = 8 : 11

Ratio between the unit price of Rs.10 and Rs.5 coins = 10 : 5 = 2 : 1

Required ratio = 8 × 2 : 11 × 1

= 16 : 11

∴ The correct answer is 16 : 11

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