[Download PDF] RPF 16 Jan 2019 Paper with Solutions

Instructions

For the following questions answer them individually

Question 111

LCM of two numbers is 63 and their HCF is 21. Given that one number is 21, find the second number.

Video Solution

Solution

Since, HCF X LCM = PRODUCT OF NUMBERS

LET THE OTHER NUMBER BE X.

SO, 21 X 63 = 21 * X

X = 63 (ANS)

Question 112

Simplify:
$$166 - [8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 18 \div 324])}]$$

Video Solution

Solution

$$166 - [8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 18 \div 324])}]$$

HERE, WE WILL USE BODMAS RULE. Bracket, Of, Division, Multiplication, Addition and Subtraction. It explains the order of operations to solve an expression.

$$166-[8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 1/18])}]$$ { solving 18/324 = 1/18}

$$166-[8^2 - 7^2 + \sqrt{(72 - 64 \div 8[1])}]$$ { solving 18*1/18}

$$166-[8^2 - 7^2 + \sqrt{(72 - 64 \div 8[1])}]$$ {solving 64/8}

$$166-[8^2 - 7^2 + \sqrt{(72 - 8)}]$$ {solving 64/8}

$$166-[8^2 - 7^2 + \sqrt{(64)}]$$ {solving 72-8}

$$166-[8^2 - 7^2 + 8]$$ {solving sqrt64}

$$166-[64-49+8]$$ {solving 72-8}

$$166-[23]$$ {solving bracket}

$$166-23$$

$$143$$

Question 113

The selling price of the article is Rs.1,980 after a successive discounts of 10% and 20%. If the cost price is 50% of the marked price, then what is the cost price. (in Rs)

Video Solution

Solution

By formula, SP = MP[1-D%/100} S.P. = SELLING PRICE AND M.P. = MARKED PRICE AND C.P. = COST PRICE

SP = MP [1-10/100][1-20/100]

SP = MP x 9/10 X 4/5

SP = 36 MP/50

MP = SP x 50/36

MP = 1980 x 50/36 = 2750

CP = MP/2 (GIVEN)

CP = RS. 2750/2 = RS. 1375

Question 114

A sum of Rs.8,400 invested under simple interest at rate of 11% p.a. If the amount after 5 years is been withdrawn and half of the total amount is been invested in Share market. Find the remainingamount. (in Rs)

Video Solution

Solution

AMOUNT(A) = PRINCIPAL(P) + SIMPLE INTEREST(SI)

A = P + PRT/100

A = 8400 + 8400*11*5/100 = RS. 13020

AMOUNT REINVESTED = A/2 (GIVEN)

AMOUNT REINVESTED = 13020/2 = RS. 6510

Question 115

Martin donates 13% of his Salary to organization for Visually challenged, 12% of his Salary toorphanage, 14% of his Salary to organization for Physically challenged and 16% of his Salary to the foundations for medical help. If the remaining amount Rs.19575 of Salary has been deposited in the bank for monthly expenses. Find the amount donated to organization for Visually challenged?(in Rs.)

Video Solution

Solution

LET TOTAL SALARY BE S.

SALARY GIVEN TO :

VISUALLY CHALLENGED = 13S/100

ORPHANAGE = 12S/100

PHYSICALLY CHALLENGED = 14S/100

MEDICAL HELP = 16S/100

TOTAL SALARY GIVEN = 1S+12S+14S+16S/100 = 55S/100

LEFT AMOUNT = 45S/100 = 19575 (GIVEN)

S = 43500

SO, AMOUNT DONATED TO VISUALLY CHALLENGED = 13 * 43500 / 100 = RS. 5655

Question 116

A sum of money is to be distributed among Ankit, Babu, Christo and David in the proportion of 5:4:3:2. If Christo gets Rs.117 more than David, what is Babu's share? (in Rs)

Video Solution

Solution

LET THE AMOUNT WITH ANKIT, BABU , CHRISTO (C) AND DAVID (D) BE 5X,4X,3X AND 2X RESPECTIVELY.

SINCE C = 117+ D

3X = 117 + 2X

X = 117

SO, BABU SHARE = 4X = 17*4 = 468

Question 117

The length of a floor is 125% of its breadth. If the area of floor is $$320m^2$$, what is the sum of the length and the breadth of the floor? (in m)

Video Solution

Solution

LET THE LENGTH BE L AND BREADTH BE B OF THE FLOOR.

L = 1.25 B (GIVEN)

L*B = 320

SOLVING, BOTH THE EQUATIONS, WE GET

B = 16 AND L = 20

L + B = 36 M

Question 118

The sum of three numbers is 243. If the ratio of the first to the second is 2:3 and that of the second to the third is 3:4, then the second number is

Video Solution

Solution

LET THE THREE NUMBERS IN THE ORDER BE A,B AND C.

GIVEN :

A+B+C = 243 (1)

A/B = 2/3, SO 3A = 2B

AND B/C = 3/4, SO 4B = 3C

PUTTING VALUES OF B IN EQUATION 1, WE GET

B = 81, A = 54 AND C= 108

SECOND NUMBER IS 81.

Question 119

A shopkeeper sells a product at the rate of Rs.1,710 and earns a profit of 14%. Find the amount which is equal to half of the cost price of the product. (in Rs)

Video Solution

Solution

SELLING PRICE (S.P.) = 1710

C.P. = COST PRICE

PROFIT (P) = 14%

P% = SP-CP/CP * 100

P = S/C - 1

114/100 = S/C

C = 100S/114

C= 100 * 1710/114 = 1500

SO, THE ANSWER = 1500/2 = 750

Question 120

The Loss incurred by selling an article at Rs.365 is 60% of the gain attained by selling the same article at Rs.701. Find the cost price of the article. (in Rs)

Video Solution

Solution

LET THE COST PRICE AND SELLING PRICE OF THE ARTICLE BE C AND S RESPECTIVELY.

GAIN = 701-C

LOSS = C-365

GIVEN LOSS = 60/100 GAIN

C-365 = 0.6 (701-C)

ON SOLVING , WE GET

C = 491

SO, COST PRICE = RS. 491

CAT Content

RPF 16 Jan 2019

LCM of two numbers is 63 and their HCF is 21. Given that one number is 21, find the second number.

Simplify:
$$166 - [8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 18 \div 324])}]$$

The selling price of the article is Rs.1,980 after a successive discounts of 10% and 20%. If the cost price is 50% of the marked price, then what is the cost price. (in Rs)

A sum of Rs.8,400 invested under simple interest at rate of 11% p.a. If the amount after 5 years is been withdrawn and half of the total amount is been invested in Share market. Find the remainingamount. (in Rs)

A sum of money is to be distributed among Ankit, Babu, Christo and David in the proportion of 5:4:3:2. If Christo gets Rs.117 more than David, what is Babu's share? (in Rs)

The length of a floor is 125% of its breadth. If the area of floor is $$320m^2$$, what is the sum of the length and the breadth of the floor? (in m)

The sum of three numbers is 243. If the ratio of the first to the second is 2:3 and that of the second to the third is 3:4, then the second number is

A shopkeeper sells a product at the rate of Rs.1,710 and earns a profit of 14%. Find the amount which is equal to half of the cost price of the product. (in Rs)

The Loss incurred by selling an article at Rs.365 is 60% of the gain attained by selling the same article at Rs.701. Find the cost price of the article. (in Rs)

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CAT Content

RPF 16 Jan 2019

LCM of two numbers is 63 and their HCF is 21. Given that one number is 21, find the second number.

Simplify:$$166 - [8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 18 \div 324])}]$$

The selling price of the article is Rs.1,980 after a successive discounts of 10% and 20%. If the cost price is 50% of the marked price, then what is the cost price. (in Rs)

A sum of Rs.8,400 invested under simple interest at rate of 11% p.a. If the amount after 5 years is been withdrawn and half of the total amount is been invested in Share market. Find the remainingamount. (in Rs)

A sum of money is to be distributed among Ankit, Babu, Christo and David in the proportion of 5:4:3:2. If Christo gets Rs.117 more than David, what is Babu's share? (in Rs)

The length of a floor is 125% of its breadth. If the area of floor is $$320m^2$$, what is the sum of the length and the breadth of the floor? (in m)

The sum of three numbers is 243. If the ratio of the first to the second is 2:3 and that of the second to the third is 3:4, then the second number is

A shopkeeper sells a product at the rate of Rs.1,710 and earns a profit of 14%. Find the amount which is equal to half of the cost price of the product. (in Rs)

The Loss incurred by selling an article at Rs.365 is 60% of the gain attained by selling the same article at Rs.701. Find the cost price of the article. (in Rs)

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Simplify:
$$166 - [8^2 - 7^2 + \sqrt{(72 - 64 \div 8[18 \times 18 \div 324])}]$$