[Download PDF] RPF 5 Jan 2019 Paper with Solutions

Instructions

For the following questions answer them individually

Question 61

When a number is divided by 72 it leaves a remainder 8. What will be the remainder, when the same number divided by 9.

Video Solution

Solution

When a number is divided by 72 it leaves a remainder 8, let the number be = $$72 + 8 = 80$$

Now, when 80 is divided by 9, => $$80=9\times8+8$$

Thus, remainder = 8

=> Ans - (C)

Question 62

In how many ways that 448 mobiles can be distributed equally to the students in the class?

Video Solution

Question 63

A sum of Rs.5400 invested under simple interest at rate of 8% p.a. If the amount after 5 years is withdrawn and half of the total amount is invested in Share market. Find the remaining amount.(in Rs)

Video Solution

Solution

Principal sum = Rs. 5400

Rate of interest = 8% and time period = 5 years

Simple interest = $$\frac{P\times R\times T}{100}$$

= $$\frac{5400\times8\times5}{100}=Rs.$$ $$2160$$

Thus, total amount after 5 years = $$Rs.$$ $$(5400+2160)=Rs.$$ $$7,560$$

$$\therefore$$ Remaining amount after half of the total amount is been invested in Share market = $$\frac{7560}{2}=Rs.$$ $$3780$$

=> Ans - (A)

Question 64

Find the product of two numbers, whose LCM is 65 and HCF is 8.

Video Solution

Solution

Product of the 2 numbers = Product of L.C.M. and H.C.F.

= $$65\times8=520$$

=> Ans - (A)

Question 65

The amount doubles itself under Compound interest in 3 years. In how many years will it become 128 times of it?

Video Solution

Solution

The amount gets doubled in 3 years.

In case of compound interest, the amount will become $$2^n$$ times in $$3n$$ years

=> Final amount = $$128=(2)^7$$

Thus, after $$3\times7=21$$ years, amount will become 128 times.

=> Ans - (C)

Question 66

The shopkeeper added 36% of the cost price as mark up and then he gives a discount of same 36% on the marked price for a sale, then what will be the overall profit or loss percentage.

Video Solution

Solution

Let cost price = Rs. 100

=> Marked price = $$100\times(\frac{136}{100})=Rs.$$ $$136$$

Thus, selling price after discount of 36% = $$136\times\frac{100-36}{100}=Rs.$$ $$87.04$$

$$\therefore$$ Loss % = $$\frac{100-87.04}{100}\times100=12.96\%$$

=> Ans - (C)

Question 67

Total area of the square Glass Piece is 729 $$cm^2$$, which is placed on the top of a table. The width between the edge of the table and the glass piece is 9 cm wide. Find the length of the table.

Video Solution

Solution

ABCD is the table and the glass piece is placed inside.

Side of glass = $$\sqrt{729}=27$$ cm

Width between glass and table = $$9$$ cm

=> Side of table = $$9+27+9=45$$ cm

=> Ans - (A)

Question 68

The average weight of 101 Notebook in a box is 10.1 kg. When a new Notebook is added to the box the average goes to 10.2 kg. Find the weight of the new Notebook.

Video Solution

Solution

Average weight of 101 Notebooks in a box = 10.1 kg

=> Total weight = $$101\times10.1=1020.1$$ kg

Let weight of new book = $$x$$ kg

=> New average = $$\frac{1020.1+x}{102}=10.2$$

=> $$1020.1+x=102\times10.2=1040.4$$

=> $$x=1040.4-1020.1=20.3$$ kg

=> Ans - (D)

Question 69

A bulb producing company found that 11% of the overall product is defective. If the number of non defective products is 5607 then find the number of defective products.

Video Solution

Solution

% of non defective products = $$89\%\equiv5607$$

=> Number of defective products = $$11\%\equiv\frac{5607}{89}\times11$$

= $$63\times11=693$$

=> Ans - (C)

Question 70

A train takes 67 seconds to cross a bridge of length 266 m. If the same train takes 29 seconds to cross a sign board, find the length of the train.

Video Solution

Solution

Let length of train = $$l$$ m and speed = $$s$$ m/s

Speed of train which takes 67 seconds to cross a bridge of length 266 m = $$s=\frac{266+l}{67}$$ -----------(i)

Also, $$s=\frac{l}{29}$$ --------------(ii)

Substituting value of $$s$$ from equation (ii) in (i), we get :

=> $$\frac{l}{29}=\frac{266+l}{67}$$

=> $$67l=(266\times29)+29l$$

=> $$67l-29l=38l=266\times29$$

=> $$l=\frac{266\times29}{38}=203$$

$$\therefore$$ Length of train = 203 m

=> Ans - (A)

CAT Content

RPF 5 Jan 2019

When a number is divided by 72 it leaves a remainder 8. What will be the remainder, when the same number divided by 9.

In how many ways that 448 mobiles can be distributed equally to the students in the class?

A sum of Rs.5400 invested under simple interest at rate of 8% p.a. If the amount after 5 years is withdrawn and half of the total amount is invested in Share market. Find the remaining amount.(in Rs)

Find the product of two numbers, whose LCM is 65 and HCF is 8.

The amount doubles itself under Compound interest in 3 years. In how many years will it become 128 times of it?

The shopkeeper added 36% of the cost price as mark up and then he gives a discount of same 36% on the marked price for a sale, then what will be the overall profit or loss percentage.

Total area of the square Glass Piece is 729 $$cm^2$$, which is placed on the top of a table. The width between the edge of the table and the glass piece is 9 cm wide. Find the length of the table.

The average weight of 101 Notebook in a box is 10.1 kg. When a new Notebook is added to the box the average goes to 10.2 kg. Find the weight of the new Notebook.

A bulb producing company found that 11% of the overall product is defective. If the number of non defective products is 5607 then find the number of defective products.

A train takes 67 seconds to cross a bridge of length 266 m. If the same train takes 29 seconds to cross a sign board, find the length of the train.

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CAT Content

RPF 5 Jan 2019

When a number is divided by 72 it leaves a remainder 8. What will be the remainder, when the same number divided by 9.

In how many ways that 448 mobiles can be distributed equally to the students in the class?

A sum of Rs.5400 invested under simple interest at rate of 8% p.a. If the amount after 5 years is withdrawn and half of the total amount is invested in Share market. Find the remaining amount.(in Rs)

Find the product of two numbers, whose LCM is 65 and HCF is 8.

The amount doubles itself under Compound interest in 3 years. In how many years will it become 128 times of it?

The shopkeeper added 36% of the cost price as mark up and then he gives a discount of same 36% on the marked price for a sale, then what will be the overall profit or loss percentage.

Total area of the square Glass Piece is 729 $$cm^2$$, which is placed on the top of a table. The width between the edge of the table and the glass piece is 9 cm wide. Find the length of the table.

The average weight of 101 Notebook in a box is 10.1 kg. When a new Notebook is added to the box the average goes to 10.2 kg. Find the weight of the new Notebook.

A bulb producing company found that 11% of the overall product is defective. If the number of non defective products is 5607 then find the number of defective products.

A train takes 67 seconds to cross a bridge of length 266 m. If the same train takes 29 seconds to cross a sign board, find the length of the train.

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