Instructions

For the following questions answer them individually

Question 1

Maruti-Suzuki Company manufactures the Ciaz cars at its Manesar facility. The company employs labour and capital/machine as inputs in a 2 : 1 ratio of their quantities. The cost of one unit of labour (think it as wage per hour) is 500 rupees and the cost of one unit of capital (machine running cost per hour) is 1500 rupees. The total labour and capital cost for the monthly production is 5 crore rupees. Due to economic slowdown, the company has decided to reduce monthly production to half. Meanwhile, the labour cost has decreased by 20% and the capital cost has gone up by 20%. Find the total capital and labour cost the company would now incur for the monthly production.

Question 2

Refer to the figure given below. AB, CD and EF are three parallel paths. A person starts from AB to reach EF by moving in four steps - moving from AB to $$O_1$$ in step 1, from $$O_1$$ to CD in step 2, from CD to $$O_2$$ in step 3 and from $$O_2$$ to EF in step 4. If he takes a curved path in one step, he cannot take a curved path in the next step. In how many ways the person can reach EF from AB ?

Question 3

The product of the roots of the equation $$\sqrt[3]{11+2x}+\sqrt[3]{11-2x}=2$$ is approximately equal to:

Question 4

Sumit stays in Noida in a joint family comprising of his parents, uncle, aunt, an elder sister and a

cousin two years younger than him. Sumit completed his MBA in 2013, from a reputed B-School.

That year, the average age of Sumit's family was 41. Sumit got married in 2015 and two years after he

became father. If the average age of Sumit's family in 2019 remains same as in 2013, and Sumit is

older than his wife by 3 years, at what age did Sumit graduate MBA ?

Question 5

A fruit seller in a locality uses dishonest practice as follows:

(i) He cheats on weight by 10 percent for every 1kg weight.

(ii) He pushes up the price of fruit by 15 percent and then gives a discount of 8 percent to the buyers for every kg sold.

Find the percentage profit of the fruit seller from sale of 1kg. (Profit is defined as Revenue - Cost)

Question 6

If $$16^{x}=\frac{64}{256^{y}}$$ and $$9^{x}=\frac{9}{3^{y}}$$, then the values of x and y are respectively,

Question 7

Mr. Madhukar worked for 5 years in a multi-commodity trading company after graduating from a

reputed B-School. He then resigned from his job and started an online garment export business. For

his business Madhukar used Rs. 8,00,000/- of his own savings and borrowed Rs. 12,00,000/- from a

private sector bank in April, the beginning month of the financial year. Mean while, RBI eased repo

rate in May and banks passed on the benefits to the borrowers. As a result, Madhukar borrowed an

additional Rs. 9,00,000/- after 4 months at an interest rate which is 10% lower than the interest rate of

his earlier borrowing. If the total interest paid by Madhukarat the end of that year on both the loans is

Rs. 1,39,200/-, what is the interest rate per annum on first borrowing ?

Question 8

In the figure, a circle of radius 2 cm is inscribed in a square. There are four smaller circles at each of

the cornerof the square. Whatis the total area covered by all the five circles ?

Question 9

Surojit Ghosh left his IT job last year and started a food business with his wife Debjani. They named

the business "Bong's Kitchen". Surojit takes $$4\frac{1}{5}$$ hours more when he works alone compared to when

he works jointly with his wife. On the other hand, Debjani takes $$28\frac{1}{5}$$ hours more than what she takes

when she works with Surojit. How long approximately will it take, Surojit to complete the business

work alone ?

Question 10

Three friends Pradeep, Suresh and Subodh workin the same office. During an extended weekend they

decided to go together on a family trip to Corbett National Park. They started from office in their own

car but at different time and travelled in the same direction at speeds of 50 km/hr, 60 km/hr and 75

km/hr respectively. Suresh and Subodh overtook Pradeep at the same point. If Suresh started 90

minutes after Pradeep, how many minutes after Pradeep did Subodh start from the office?

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