Crash Course Math Day 9

Mathematics Miscellaneous Quiz
Q1. A naughty student breaks the pencil in such a way that the ratio of two broken parts is same as
that of the original length of the pencil to one of the large part of the pencil. The ratio of the other
part to the original length of pencil is:
(a) 1 : 2√5
(b) 2 : (3 + √5)
(c) 2 : √5
(d) Can’t be determined
Q2. A student obtained equal marks in History and Sociology. The ratio of marks in Sociology and
Geography is 2 : 3 and the ratio of marks in History and Philosophy is 1 : 2. If he has scored an
aggregate of 55% marks. The maximum marks in each subject it same. In how many subjects did
he score equal to or greater than 60% marks?
(a) 1
(b) 2
(c) 3
(d) None of these
Q3. The ratio of income of Anil and Mukesh is 2 : 3. The sum of their expenditure is Rs. 8000 and
the amount of savings of Anil is equal to the amount of expenditure of Mukesh. What is the sum of
their savings?
(a) 22,000
(b) 4,000
(c) 16,000
(d) 12,000
Q4. Hutch and Essar entered into a partnership just 5 months ago. The ratio of profit claimed by
Hutch and Essar is 6 : 17. If Essar had just started his business 12 months ago with Rs. 1275, what
is the amount contributed by Hutch?
(a) Rs. 980
(b) Rs. 1080.
(c) Rs. 1200.
(d) Rs. 998
Q5. The concentration of petrol in three different mixtures

𝟏 𝟑 𝟒
(petrol and kerosene) is 𝟐, 𝟓 and 𝟓 respectively. If 2 litres, 3 litres
and 1 litre are taken from these three different vessels and
mixed. What is the ratio of petrol and Kerosene in the new
mixture?
(a) 4 : 5
(b) 3 : 2
(c) 3 : 5
(d) 2 : 3
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Q6. There are two vessels containing the mixture of milk and water. In the first vessel the water is
2/3 of the milk and in the second vessel water is just 40% of the milk. In what ratio these are
required to mix to make 24 litres mixture in which the ratio of water is to milk is 1 : 2?
(a) 4 : 3
(b) 5 : 7
(c) 5 : 2
(d) 7 : 5
Q7. 6 pumps of Kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same
tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a UHSA pump?
(a) 6 : 7
(b) 7 : 6
(c) 7 : 54
(d) Can’t be determined
Q8. The ratio of prices of Cello and Rotomac pens in 2000 were in the ratio of 3 : 5. In 2005 the
price of Cello pen trebles itself and the price of Rotomac pen is increased by Rs. 100, then the new
ratio of prices of the same pens becomes 4 : 5. What was the original price of the Rotomac pen in
2000?
(a) Rs. 60
(b) Rs. 80
(c) Rs. 100
(d) Rs. 120.
Q9. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the
Dew and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to
achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).
(a) 10 : 3
(b) 4 : 1
(c) 3 : 10
(d) 3 : 1
Q10. Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4:1. When his naughty
child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2.
What is the total amount of the crushed grapes?
(a) 0.5 kg
(b) 1 kg
(c) 0.75 kg
(d) None of these

Solutions
S1. Ans.(b)
Sol. Let length of pencil x & length of broken parts is a & b
𝑥 𝑎
=
𝑎 𝑏
x=a+b
𝑎+𝑏 𝑎
=
𝑎 𝑏
ab + b² = a²
a² – b² – ab = 0 …(i)
Let b = 1
a:b=a:1
Putting b = 1 in (i)
a² – 1 – a = 0
a² – a – 1 = 0
Using quadratic
−𝑏 ± √𝑏 2 − 4𝑎𝑐
𝑎=
2𝑎
1 + √1 + 4
𝑎=
2
1 + √5
𝑎=
2
1 + √5
𝑎∶𝑏= ∶1
2
= 1 + √5 ∶ 2
x = a + b = 2 + 1 + √5
= 3 + √5
b : x = 2 : 3 + √5
S2. Ans.(b)
Sol.
H : So → 1:1
S : Geo → 2 : 3
History : Pil → 1: 2
H :S: G : P → 2 : 2 :3: 4
⇒ 2x, 2x, 3x, 4x
Total marks ⇒ 2x + 2x + 3x + 4x
⇒ 11x
Maximum marks in each subject are equal
11
∴ Aggregate % = 𝑥
4

ATQ,
11
𝑥 = 55
4
x = 20
History → 40
Sociology → 40
Geography → 60
Philosophy → 80
Hence in two subjects he scored more than equal to 60%
S3. Ans.(d)
Sol. Income → Anil : Mukesh → 2 : 3
Anil → 2x
Mukesh → 3x
Let savings of Anil → K
Then Expenditure of M → K
Expenditure of A = 2x – K
2x – k + k = 800
2x = 8000
x = 4000
Total Income of A + B
= 5x = 20000
Total saving of A & B = 20000 – 8000
= 12000 Rs.
S4. Ans.(b)
Sol.
Profit of Hutch time × amount of H
=
Profit of Essar time × amount of E
6 5×𝑘
=
17 12 × 1275
k = 1080
S5. Ans.(b)
Sol. Concentration of Petrol
1 3 4
→ , ,
2 5 5
  
2L 3L 1L

P → 1 → 1.8 → 0.8
Total P → 1 + 1.8 + 0.8 → 3.6L
Total K = (2 + 3 + 1) – 3.6
= 6 – 3.6 = 2.4
Ratio = 3.6 : 2.4 = 3 : 2
S6. Ans.(b)
Sol. Stressed Milk : Water
2
1→ x: 3𝑥
3:2
2
Water → 5
2nd → 100 : 40
5:2
2
Water ⇒ 7
2 2
:
5 7
1
3
1 2 2 1
− : −
3 7 5 3
(5 : 7)
S7. Ans.(a)
1
Sol. Efficiency of 6 K Pumps → 7
1 1
Efficiency of 1 K Pumps → 7 × 6 = 42
1
Efficiency of 2 Usha pumps = 18
1
Efficiency of 1 usha pump = 36
1 1
Ratio = 42 ∶ 36
=6:7
S8. Ans.(b)
Sol. Cello : Rotomac
2000 → 3 : 5
Cello → 3x
Rotomac → 5x
2005 → Cello → 3x × 3 = 9x
Rotomac → 5x + 100
9𝑥 4
=
5𝑥 + 100 5
45x = 20x + 400
25x = 400
x = 16
Rotomac = 5 × 16= 80 Rs.

S9. Ans.(a)
Sol. D : S
M₁ → 7 : 3
M₂ → 5 : 4
Resultant → 2 : 1
Dew in M1 Dew in M 2
7 5
10 9
2
3
2 5 7 2
− : −
3 9 10 3
1 1
:
9 30
10 : 3
S10. Ans.(c)
Sol.
Water : Pulp
Fresh → 4 : 1 2
Crushed → 3 : 2
8:2
3:2
10r → 1.5
1r → 0.15
Weigh of grapes crushed = (8 – 3) r
= 5r
= 5 × 0.15
= 0.75 kg

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Mathematics Miscellaneous Quiz

Q5. The concentration of petrol in three different mixtures

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