AAO ExamCT 5: Quant (Ratio and Proportion)
AAO ExamCT 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?

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

120 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

Rs. 1100

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.

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

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.

12

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

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.7,400

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. 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

4 : 7

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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