# Arithmetic - Ratio, Proportion & Variation - Previous Year CAT/MBA Questions

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Here we bring you all previous year Arithmetic - Ratio, Proportion & Variation cat questions along with detailed solutions.

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**IIFT 2014 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

What is the least cost way to reach to VIZAG from KOCHI?

- (a)
Take a flight from KOCHI to VIZAG

- (b)
Take a ship from KOCHI to CHENNAI and then take a train to VIZAG

- (c)
Take a train from KOCHI to KANYKUMARI and then take a ship to VIZAG

- (d)
Take a train from KOCHI to MUMBAI and then take a flight to VIZAG

Answer: Option B

**Text Explanation** :

Considering the cost in each option.

Option 1: (600 × 5) = 3000

Option 2: (901 × 1.5) + (300 × 2.5) ≈ 2100

Option 3: (1100 × 2.5) + (250 × 1.5) > 2100

Option 4: (300 × 2.5) + (500 × 5) > 2100

Hence, option (b).

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**IIFT 2014 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

Ravindra and Rekha got married 10 years ago, their ages were in the ratio of 5 : 4. Today Ravindra’s age is one sixth more than Rekha’s age. After marriage, they had 6 children including a triplet and twins. The age of the triplets, twins and the sixth child is in the ratio of 3 : 2 : 1. What is the largest possible value of the present total age of the family?

- (a)
79

- (b)
93

- (c)
101

- (d)
107

Answer: Option D

**Text Explanation** :

Let the present age of Ravindra and Rekha be R_{v} and R_{e} respectively.

$\frac{{R}_{v}-10}{{R}_{e}-10}$ = $\frac{5}{4}$

R_{v} = (1 + 1/6)R_{e}

Solving these equations, we get R_{v} = 35 and R_{e} = 30

Maximum age of a child = 9 years (10 year after marriage)

To maximize the age of family,

Age of triplets = 9 years, twins = 6 years and sixth child = 3 years

Age of the family = 35 + 30 + (9 × 3) + (6 × 2) + 3 = 107

Hence, option (d).

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**XAT 2012 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing Rs. 4000 and Rs. 6000 respectively. The conditions of partnership were as follows:

- In case of profits till Rs. 200,000 per annum, profits would be shared in the radio of the invested capital.
- Profits from Rs. 200,001 till Rs. 400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
- Profits in excess of Rs. 400,000, Shyam would take 35% out of the profits beyond Rs. 400,000, before the division of remaining profits, which will then be based on ratio of invested capital.

If Shyam’s share in a particular year was Rs. 367000, which option indicates the total business profit (in Rs.) for that year?

- (a)
520,000

- (b)
530,000

- (c)
540,000

- (d)
550,000

- (e)
None of the above

Answer: Option D

**Text Explanation** :

For first Rs. 200000, Shyam gets, 6000/(4000 + 6000) × 100 = 60% of the profit.

For next Rs. 200000, he gets 20% + plus 60% of the remaining profit.

i.e. 20% + 80 × 0.6% = 68%

Similarly, for a profit margin greater than Rs. 400000, he will get, 35% + 65 × 0.6% = 74% of the profits beyond Rs. 400000

Now, for a profit of first Rs. 400000, Shyam will receive 200000 × (68 + 60)/100 = 256000

But Shyam earns a total profit of 367000.

Let total profit earned by them be Rs. 400000 + x.

Hence, Shyam received 367000 – 256000 = Rs. 110000 from Rs. x profit.

i.e. Rs. 110000 is 74% of x.

Hence, x = 110000/0.74 = 150000

Hence, total profit earned by them = 400000 + 150000 = Rs. 550000

Hence, option (d).

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**IIFT 2012 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

A sum of Rs.1400 is divided amongst A, B, C and D such that A's share : B's share = B's share : C's share = C's share : D's share = $\frac{3}{4}$

How much is C’s share?

- (a)
Rs.72

- (b)
Rs.288

- (c)
Rs.216

- (d)
Rs.384

Answer: Option D

**Text Explanation** :

A : B = 3 : 4, B : C = 3 : 4, C : D = 3 : 4

∴ A : D = ${\left(\frac{3}{4}\right)}^{3}$ = $\frac{27}{64}$

Let D = 64

Then, C = $\frac{3}{4}$ × 64 = 48

B = $\frac{3}{4}$ × 48 = 36

A = $\frac{3}{4}$ × 36 = 27

∴ A : B : C : D = 27 : 36 : 48 : 64

∴ C's share = $\left\{\frac{48}{27+36+48+64}\right\}$ × 1400 = Rs. 384

Hence, option (d).

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**IIFT 2011 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

While preparing for a management entrance examination Romit attempted to solve three paper, namely Mathematics, Verbal English and Logical Analysis, each of which have the full marks of 100. It is observed that one-third of the marks obtained by Romit in Logical Analysis is greater than half of his marks obtained in Verbal English By 5. He has obtained a total of 210 marks in the examination and 70 marks in Mathematics. What is the difference between the marks obtained by him in Mathematics and Verbal English?

- (a)
40

- (b)
10

- (c)
20

- (d)
30

Answer: Option C

**Text Explanation** :

Let Romit score l and v marks in Logical Analysis and Verbal English respectively.

∴ l + v + 70 = 210

∴ l + v = 140 …(i)

Now, $\frac{l}{3}$ = $\frac{v}{2}$ + 5 ...(ii)

Solving i and ii, we get,

l = 90, and v = 50

Hence, required difference = 70 – 50 = 20

Hence, option (c).

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**IIFT 2011 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

Aniket and Animesh are two colleagues working in PQ Communications, and each of them earned an investible surplus of Rs. 1, 50, 000/- during a certain period. While Animesh is a risk-averse person, Aniket prefers to go for higher return opportunities. Animesh uses his entire savings in Public Provident Fund (PPF) and National Saving Certificates (NSC). It is observed that one-third of the savings made by Animesh in PPF is equal to one-half of his savings in NSC. On the other hand, Aniket distributes his investible funds in share market, NSC and PPF. It is observed that his investments in share market exceeds his savings in NSC and PPF by Rs. 20,000/- and Rs. 40,000/- respectively. The difference between the amount invested in NSC by Animesh and Aniket is:

- (a)
Rs. 25,000/-

- (b)
Rs. 15,000/-

- (c)
Rs. 20,000/-

- (d)
Rs. 10,000/-

Answer: Option D

**Text Explanation** :

Let Animesh invest Rs. a in PPF and Rs. b in NSC.

∴ $\frac{a}{3}$ = $\frac{b}{2}$

Also, a + b = 150000

∴ 5b/2 = 150000

∴ b = 60000

Let Aniket invest Rs. x in PPF.

∴ He invests Rs. (x + 40000) in shares and Rs. (x + 20000) in NSC.

Also, x + x + 40000 + x + 20000 = 150000

∴ x = 30000

∴ Aniket’s investment in NSC = Rs. 50000

Animesh’s investment in NSC = Rs. 60000

∴ Difference = Rs. 10000

Hence, option (d).

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**IIFT 2010 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

A small confectioner bought a certain number of pastries flavoured pineapple, mango and black-forest from the bakery, giving for each pastry as many rupees as there were pastry of that kind; altogether he bought 23 pastries and spent Rs.211; find the number of each kind of pastry that he bought, if mango pastry are cheaper than pineapple pastry and dearer than black-forest pastry.

- (a)
(10, 9, 4)

- (b)
(11, 9, 3)

- (c)
(10, 8, 5)

- (d)
(11, 8, 4)

Answer: Option B

**Text Explanation** :

Let p, m and b be the number of pineapple, mango and black-forest pastries respectively.

∴ p + m + b = 23 … (i)

Each pastry cost as many rupees as there were pastries of that kind.

∴ p^{2} + m^{2} + b^{2} = 211 … (ii)

Substituting options in (i) and (ii), we find that only option 2 satisfies both the equations

Hence, option (b).

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**IIFT 2009 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

Kartik’s mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denomination of 1 Rupee, 2 Rupee and 5 Rupee coins. Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins and in return receives the same number of 1 Rupee coins. Next he goes to a dairy shop to buy milk and butter and gives all 2 Rupee coins and in return gets thirty 5 Rupee coins which increases the number of 5 Rupee coins to 75% more than the original number. If the number of 1 Rupee coins now is 50, the number of 1 Rupee and 5 Rupee coins originally were:

- (a)
10, 60

- (b)
10, 70

- (c)
10, 80

- (d)
None of the above

Answer: Option D

**Text Explanation** :

Let Kartik initially have x, y and z, 1 Rupee, 2 Rupee and 5 Rupee coins respectively.

At the grocery shop, the number of 5 Rupee coins becomes z/2 and the number of 1 rupee coins becomes x + z/2

At the dairy, the number of 5 Rupee coins changes to z/2 + 30

By conditions given in the question,

z/2 + 30 = 1.75z

∴ z = 24

Also, x + z/2 = 50

∴ x = 38

Hence, option (d).

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**IIFT 2009 QA | Arithmetic - Ratio, Proportion & Variation cat Question**

Find the ratio of shaded area to unshaded area.

- (a)
$\frac{1}{5}$($\sqrt{21}$ - 2)

- (b)
$\frac{1}{5}$(3$\sqrt{7}$ - 2)

- (c)
$\frac{1}{5}$(3$\sqrt{7}$ - 2$\sqrt{3}$)

- (d)
None of the above

Answer: Option D

**Text Explanation** :

Area of shaded pentagon = $\frac{5}{4}$$\left(\sqrt{1+\frac{2}{\sqrt{5}}}\right){a}^{2}$

Area of 5, unshaded equilateral triangles = 5 × $\frac{\sqrt{3}}{4}{a}^{2}$

∴ Ratio of shaded area to unshaded area = $\frac{{\displaystyle \frac{5}{4}}\left(\sqrt{1+{\displaystyle \frac{2}{\sqrt{5}}}}\right){a}^{2}}{5\times {\displaystyle \frac{\sqrt{3}}{4}}{a}^{2}}$ = $\sqrt{\frac{1}{3}+\frac{2}{3\sqrt{5}}}$

None of the option is right.

Hence, option (d).

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