# Areas Quiz Set 010

### Question 1

The diagonal and one side of a rectangle are 17 m and 15 m. What is the percentage saving of a man who walks along the diagonal instead of the two sides?

A

\$26{2/23}\$%.

B

\$28{7/22}\$%.

C

\$23{2/25}\$%.

D

\$26{19/25}\$%.

Soln.
Ans: a

The side = \$√{17^2 - 15^2}\$ = \$√{289 - 225}\$ = 8. So the saving = (15 + 8) - 17 = 6 meters. So the %-age saving is \$6/23\$ × 100 = \${600/23}\$, which is same as: \$26{2/23}\$%.

### Question 2

The length of a square is increased by 4%, what is the % increase in area?

A

8.16%.

B

17%.

C

11%.

D

16.32%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 4, the increase is \$(2 × 4 + 4^2/100)\$% = 8.16%

### Question 3

What is the smallest number of square tiles that can be laid fully, without cutting, on a floor 10 m by 64 m?

A

160 .

B

161 .

C

159 .

D

162 .

Soln.
Ans: a

The side of the square tile has to be HCF(10, 64) = 2. Hence, the required number is \${10 × 64}/{2 × 2}\$ = 160.

### Question 4

A rectangular wire 26 × 9 is re-aligned into a rectangle 13 × 27. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 5

What is the cost of plastering, @50 paise per square meter, the walls and floor of a 26 m × 6 m. tank that is 8 meters high?

A

Rs. 334 .

B

Rs. 336 .

C

Rs. 332 .

D

Rs. 338 .

Soln.
Ans: a

The area to be plastered is \$(2 × l × h) + (2 × b × h) + (l × b)\$ = (2 × 26 × 8) + (2 × 6 × 8) + (26 × 6) = 668 sq. m. The cost = 668 × 0.50 = Rs. 334.