IIFT 2011 Question Paper

It is given that a man is able to perform the work equal to the same done by 2 boys. Hence, we can assume that In Bilaspur village 21=(12+18/2) men completed construction of a primary health center in 60 days, by working for 7.5 hours a day. 

Hence, total men hours required to completed the primary health center in Bilaspur = 7.5*21*60 = 9450. 

Let us assume that 'n' be the number of boys required to help 21 men to complete the work in Harigarh in 50 days by working 9 hours a day. 

Therefore, we can say that

$$\Rightarrow$$ 2*9450 = 50*9*(21+t/2) 

$$\Rightarrow$$ 42 = 21+t/2

$$\Rightarrow$$ t = 42 

Hence, option D is the correct answer. 

$$(\sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}})\div\sqrt{\frac{16}{81}}=x$$ This can be simplified as

$$(\frac{15}{27}-\frac{5}{12})\div\frac{4}{9}=x$$

$$(\frac{5}{36})*\frac{9}{4}=x$$

x=$$\frac{5}{16}$$. Hence, option A is the correct answer.

Given that If $$\frac{x}{y}=\frac{7}{4}$$

Therefore, $$(\frac{x}{y})^2=\frac{49}{16}$$ ... (1)

$$\dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}$$ this can be written as, 

$$\Rightarrow$$ $$\dfrac{(\frac{x}{y})^2-1}{(\frac{x}{y})^2+1}$$

$$\Rightarrow$$ $$\dfrac{\frac{49}{16}-1}{\frac{49}{16}+1}$$

$$\Rightarrow$$ $$\dfrac{49-16}{49+16}$$

$$\Rightarrow$$ $$\dfrac{33}{65}$$

Hence, option C is the correct answer.

Let 'a' and 'b' be the marks obtained by Romit in Verbal English and Logical Analysis respectively. It is given that,

a + b + 70 = 210

a + b = 140.  ... (1) 

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.

$$\dfrac{b}{3} - \dfrac{a}{2} = 5$$

$$2b - 3a = 30$$   ... (2)

On solving equation (1) and (2) we get b = 90 and a = 50. 

  Hence, the difference between the marks obtained by him in Mathematics and Verbal English = 70 - 50 = 20.

Therefore, option C is the correct answer.

Let 'x' be the amount invested by Aniket in share market. Therefore, amount invested by him in NSC and PPF will be 'x-20000' and 'x-40000' respectively. 

It is given that, x + x-20000 + x-40000 = 150000

$$\Rightarrow$$ x = 70000. 

Hence, the amount invested by Aniket in NSC = x - 20000 = 50000. 

It is given that one-third of the savings made by Animesh in PPF is equal to one-half of his savings in NSC.

Let 'y' be the amount invested by Animesh in NSC. Then we can say that he invested '150000-y' in PPF.

$$\Rightarrow$$ $$\dfrac{150000-y}{3} = \dfrac{y}{2}$$

$$\Rightarrow$$ $$300000-2y = 3y$$

$$\Rightarrow$$ $$y = 60000$$

Therefore, the difference between the amount invested in NSC by Animesh and Aniket = 60000 - 50000 = Rs. 10000. Hence, option D is the correct answer.

Let 'x' and 'y' be the average price of 13 books obtained from MN Distributors and remaining 2 books purchased from UV Publishers respectively. 

It is given that he spent a total of Rs. 4500. Therefore, 

13x + 2y = 4500 ... (1) 

It is also observed that one-sixth of the average price of all the 15 books purchased is equal to one-fifth of the average price of the 13 books obtained from MN Distributors.

$$\dfrac{4500/15}{6} = \dfrac{x}{5}$$

$$x = 250$$ ... (2)

Form equation (1) and (2) we can say that 2y = 1250.

Let 'a' and 'b' be the price of two books purchased from UV Publishers. It is given that one-third of the price of one volume is equal to one-half of the price of the other.

Therefore, $$\dfrac{a}{3} = \dfrac{b}{2}$$ ... (3) 

Also, $$2y = 1250 = a + b$$ ... (4)

From, equation (3) and (4) we can say that a = 750 and b = 500. Hence, option C is the correct answer. 

Let 'A', 'S' and 'P' be Amita's, Sumita's and Paramita's present age. 

It is given that 2 years ago, one-fifth of Amita’s age was equal to one-fourth of the age of Sumita, and the average of their age was 27 years.

$$\dfrac{(A-2)+(S-2)}{2} = 27$$

$$A+S = 58$$  ... (1)

Also, $$\dfrac{A-2}{5} = \dfrac{S-2}{4}$$

$$4A-8 = 5S-10$$

$$5S - 4A = 2$$ ... (2) 

From equation (1) and (2) we can say that S = 26, A = 32.

Average age of Amita, Sumita and Paramita before 2 years = 24. 

 $$\dfrac{(A-2)+(S-2)+(P-2)}{3} = 24$$

 $$A+S+P = 78$$. Hence, P = 20.

Therefore, the average age of Sumita and Paramita 3 years from now? = $$\dfrac{(S+3)+(P+3)}{2}$$ = $$\dfrac{(26+3)+(20+3)}{2}$$ = 26 years.

Hence, option B is the correct answer.

Let 'G' be the value of the gift. Hence, the monthly salary of domestic help = $$\dfrac{90+G}{12}$$. 

Therefore, $$9*\dfrac{90+G}{12} = G+65$$

$$3G = 30$$. Hence, G = Rs. 10.

Let 'a', 'b', 'c' and 'd' be the prime number in ascending order. The product of the first three is 7429 and last three is 12673. Find the first number.

Given that $$a*b*c =  7429$$ and $$b*c*d =  12673$$

Therefore, $$\dfrac{b*c*d}{a*b*c} = \dfrac{12673}{7429}$$ 

$$\Rightarrow$$ $$\dfrac{d}{a} = \dfrac{29}{17}$$

Since a and d are prime number there won't be any common factor which can divide both. Hence, a = 17, b = 19, c = 23 and d = 29. 

Therefore, option B is the correct answer.   

When the paper is rolled along its length, the circumference of the cylinder formed is equal to the length and the height is equal to the breadth of the rectangle.

Let 'r' be the radius and 'h' be the height of the cylinder formed. 

$$2\pi*r = 22$$ and h = 10

Hence, the volume of the cylinder = $$\pi*r^2*h$$ = $$\dfrac{22}{7}*(7/2)^2*10$$ = 385 $$cm^3$$.