# PE 1 - Ratio | Ratio, Proportion and Partnership

**PE 1 - Ratio | Ratio, Proportion and Partnership**

Two natural numbers are in the ratio 12 : 5 and the sum of their squares is 676. What are the numbers?

- A.
12 and 5

- B.
24 and 10

- C.
36 and 15

- D.
48 and 20

Answer: Option B

**Explanation** :

Let the numbers be 12x and 5x.

⇒ (12x)^{2} + (5x)^{2} = 676

⇒ 144x^{2} + 25x^{2} = 676

⇒ 169x^{2} = 676

⇒ x^{2} = 4

⇒ x = 2

∴ The numbers are 24 and 10.

Hence, option (b).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

What is the third proportional to 18 and 8?

- A.
10

- B.
26

- C.
12

- D.
4

Answer: Option C

**Explanation** :

Let the 3rd proportion to 18 and 8 be x.

⇒ $\frac{18}{\mathrm{x}}=\frac{\mathrm{x}}{8}$

⇒ x^{2} = 144

⇒ x = 12

Hence, option (c).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

Ram and Shyam invest Rs. 30,000 and Rs, 25,000 in a gym. If the gym earns Rs. 110,000 in one year, what amount does Shyam get?

- A.
Rs. 45,000

- B.
Rs. 60,000

- C.
Rs. 50,000

- D.
None of these

Answer: Option C

**Explanation** :

Ratio of profits of Ram and Shyam will be same as the ratio of their investments.

⇒ P_{R} : P_{S} = 30000 : 25000 = 6 : 5

∴ PS = 5/(6+5) × 110000 = 50,000

Hence, option (c).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

The largest number amongst $\frac{17}{12}$, $2\frac{5}{9}$, $\frac{27}{11}$ and $2\frac{8}{9}$ is

- A. $\frac{17}{12}$
- B. $2\frac{5}{9}$
- C. $\frac{27}{11}$
- D. $2\frac{8}{9}$

Answer: Option D

**Explanation** :

The given fractions are $\frac{17}{12}$, $2\frac{5}{9}$, $\frac{27}{11}$ and $\frac{26}{9}$ is

Of the 4 fractions 17/12 is less than 2 while rest are greater than 2. Hence, 17/12 is not the highest fraction.

Of the remaining three 26/9 is definitely greater than 23/9.

∴ One of 27/11 or 26/9 is greater.

Now, $\frac{27}{11}$ = $\frac{243}{99}$

and, $\frac{26}{9}$ = $\frac{286}{99}$

⇒ 26/9 i.e., $2\frac{8}{9}$ is the greatest of the given fractions.

Hence, option (d).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

Two numbers are in the ratio 5 : 6. If 8 is added to both, their ratio changes to 3 : 4. What is the value of the larger number?

- A.
12

- B.
24

- C.
10

- D.
20

Answer: Option B

**Explanation** :

Let the numbers be 5x and 6x respectively.

Now, $\frac{5x+8}{6x+8}=\frac{3}{4}$

⇒ 20x + 32 = 18x + 24

⇒ 2x = 8

⇒ x = 4

∴ The larger number is 6x = 24

Hence, option (b).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

A person distributed Rs. 1872 among Arpit, Romesh and Jitesh such that 8 times Romesh's share is equal to 12 times Jitesh's share or 3 times Arpit's share. How much does Romesh get?

- A.
Rs. 560

- B.
Rs. 495

- C.
Rs. 432

- D.
Rs. 544

Answer: Option C

**Explanation** :

Let their shares be A, R and J respectively.

∴ 8R = 12J = 3A

⇒ J = 2R/3 and A = 8R/3

Also, A + R + J = 1872

⇒ 8R/3 + R + 2R/3 = 1872

⇒ 13R/3 = 1872

⇒ R = 1872 × 3/13 = 432

Hence, option (c).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

A bag can contain either 72 mangoes or 30 bananas. If the bag has 48 mangos, how many bananas can it now carry?

- A.
10

- B.
12

- C.
18

- D.
14

Answer: Option A

**Explanation** :

The bag already contains 48 mangoes, hence it has capacity for 24 more mangoes.

Now, 72 mangoes are equivalent to 30 bananas.

⇒ 24 mangos are equivalent to 10 bananas.

Hence, instead of 24 more mangoes, 10 bananas can be carried in the bag.

Hence, option (a).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

If a : b = 5 : 4 and b : c = 6 : 11, what is the value of (2a + 2c) : (2b - a)?

- A.
37 : 4

- B.
74 : 9

- C.
46 : 25

- D.
32 : 19

Answer: Option B

**Explanation** :

Given, a : b = 5 : 4 and b : c = 6 : 11

∴ a : b : c = 5 × 3 : 12 : 11 × 2 = 15 : 12 : 22

⇒ $\frac{2a+2c}{2b-a}$ = $\frac{30x+44x}{24x-15x}$ = $\frac{74}{9}$

Hence, option (b).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

Akanksha started a business with 24,000. Swapnil joined him two months later with an investment of Rs. 16,000. In what ratio would they share the annual profit?

- A.
6 : 5

- B.
5 : 6

- C.
9 : 5

- D.
5 : 9

Answer: Option C

**Explanation** :

$\frac{{P}_{Akanksha}}{{P}_{Swapnil}}$ = $\frac{{I}_{Akanksha}\times {T}_{Akanksha}}{{I}_{Swapnil}\times {T}_{Swapnil}}$ = $\frac{24000\times 12}{16000\times 10}$ = $\frac{9}{5}$

Hence, option (c).

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**PE 1 - Ratio | Ratio, Proportion and Partnership**

If (a + b) : (b + c) : (c + a) = 3 : 4 : 5 and (a + b + c) = 18, what is the value of a?

- A.
3

- B.
9

- C.
8

- D.
6

Answer: Option D

**Explanation** :

Let a + b = 3x …(1)

b + c = 4x and …(2)

c + a = 5x …(3)

Adding all three equations, we get

⇒ 2(a + b + c) = 12x

⇒ a + b + c = 6x …(4)

(4) and (1) ⇒ c = 3x

(4) and (2) ⇒ a = 2x

(4) and (3) ⇒ b = x

Now, we also know a + b + c = 18

⇒ 2x + x + 3x = 18

⇒ x = 3

∴ a = 2x = 6

Hence, option (d).

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