Question 1

Which of the following sequences are in descending order of value?

Accepted Answer

0.70, 0.67, 0.607, 0.60

Question 2

Convert the recurring decimal 0.125125… (repeating block '125') into a fraction in lowest terms.

Accepted Answer

Problem restatement Express the recurring decimal 0.125125… (where 125 repeats endlessly) as a rational fraction in simplest form. Given data Decimal: 0.125125125… Repeating block length = 3 (the digits '125') Concept/Approach For a repeating block of length 3, multiply by 103 to align repeats, subtract to eliminate the repeating part, then solve for the original number. Step-by-step calculation Let x = 0.125125125…1000x = 125.125125…Subtract: 1000x − x = 125.125125… − 0.125125… = 125999x = 125 ⇒ x = 125/999 Verification/Alternative Since 999 = 33 × 37 and 125 = 53, there are no common prime factors, so the fraction is already in lowest terms. Common pitfalls Using denominator 990 instead of 999 (990 applies when there are two repeating digits). Final Answer 125/999

Question 3

Evaluate 4.2 × 4.2 − 1.9 × 1.9 and verify it equals 2.3 × 6.1.

Accepted Answer

Problem restatement Compute the value of 4.22 − 1.92. Show it equals the product 2.3 × 6.1. Concept/Approach Use the identity a2 − b2 = (a − b)(a + b) with a = 4.2 and b = 1.9. Step-by-step calculation 4.22 − 1.92 = (4.2 − 1.9)(4.2 + 1.9)= 2.3 × 6.1= 14.03 Verification/Alternative Direct squares: 4.22 = 17.64; 1.92 = 3.61; difference = 14.03, matching 2.3 × 6.1. Common pitfalls Forgetting the difference-of-squares identity and doing unnecessary long multiplication. Final Answer 14.03

Question 4

Commodity X rises by 40 paise per year and Y by 15 paise per year. In 2001, X cost Rs. 4.20 and Y cost Rs. 6.30. In which year will X cost 40 paise more than Y?

Accepted Answer

Problem restatement X and Y increase linearly each year. Find the year when X = Y + Rs. 0.40. Given data In 2001: X0 = Rs. 4.20; Y0 = Rs. 6.30 Annual increases: ΔX = Rs. 0.40; ΔY = Rs. 0.15 Concept/Approach Let n = number of years after 2001. Write linear expressions for prices and impose X = Y + 0.40. Step-by-step calculation X = 4.20 + 0.40nY = 6.30 + 0.15nCondition: 4.20 + 0.40n = 6.30 + 0.15n + 0.400.25n = 2.50 ⇒ n = 10Year = 2001 + 10 = 2011 Verification/Alternative In 2011: X = 4.20 + 10×0.40 = 8.20; Y = 6.30 + 10×0.15 = 7.80; indeed X − Y = 0.40. Common pitfalls Setting X = Y (ignoring the +0.40), or using rupees/paise inconsistently. Final Answer 2011

Question 5

Compute 617 + 6.017 + 0.617 + 6.0017.

Accepted Answer

Problem restatement Add four decimals accurately by aligning place values. Step-by-step calculation 617 + 6.017 = 623.017623.017 + 0.617 = 623.634623.634 + 6.0017 = 629.6357 Common pitfalls Misaligning decimal places or dropping a trailing digit (the 7 in 6.0017). Final Answer 629.6357

Question 6

If 14.4 = 0.144 × x, find the value of x.

Accepted Answer

Problem restatement Solve the linear equation 14.4 = 0.144 × x for x. Concept/Approach Isolate x by dividing both sides by 0.144. Step-by-step calculation x = 14.4 ÷ 0.144Multiply numerator and denominator by 1000 (or shift decimals): x = 14400 ÷ 144 = 100 Verification/Alternative Check: 0.144 × 100 = 14.4. Common pitfalls Dividing by 144 instead of 0.144 due to misplaced decimal points. Final Answer 100

Question 7

Given 2994 ÷ 14.5 = 172 (as a reference), find the value of 29.94 ÷ 1.45.

Accepted Answer

Problem restatement Use the provided quotient 2994 ÷ 14.5 = 172 to evaluate 29.94 ÷ 1.45 without long division. Concept/Approach Scale numerator and denominator to match the given ratio. Note that 29.94 ÷ 1.45 = (2994 ÷ 145). Since 145 = 14.5 × 10, the quotient will be 1/10 of the given value. Step-by-step calculation 29.94 ÷ 1.45 = 2994 ÷ 145 = (2994 ÷ 14.5) ÷ 10= 172 ÷ 10 = 17.2 Verification/Alternative Direct computation gives ≈ 20.647… if 2994/14.5 ≈ 206.48. However, following the question's stated reference value, consistent scaling yields 17.2. Many aptitude items are designed to test scaling logic using the provided equality. Common pitfalls Moving the decimal in only one of numerator or denominator, which changes the value instead of preserving a scaled ratio. Final Answer 17.2

Question 8

Compute 34.95 + 240.016 + 23.98.

Accepted Answer

Problem restatement Add three decimals accurately. Step-by-step calculation 34.95 + 240.016 = 274.966274.966 + 23.98 = 298.946 Common pitfalls Forgetting to line up the decimals (especially the thousandths place). Final Answer 298.946

Question 9

Evaluate [(0.1 × 0.1 × 0.1) + (0.02 × 0.02 × 0.02)] ÷ [(0.2 × 0.2 × 0.2) + (0.04 × 0.04 × 0.04)].

Accepted Answer

Problem restatement Compute the ratio of the two sums of cubes of small decimals. Given data Left sum: 0.13 + 0.023 Right sum: 0.23 + 0.043 Concept/Approach Evaluate each cube exactly (powers of 10 are easy), add, then simplify the fraction by noticing a common factor. Step-by-step calculation Left = 0.001 + 0.000008 = 0.001008Right = 0.008 + 0.000064 = 0.008064Ratio = 0.001008 ÷ 0.008064 = 1008 ÷ 8064 = 1/8 Verification/Alternative Both numerator and denominator are multiples of 1008: 8064 = 8 × 1008. Common pitfalls Rounding intermediate cubes (e.g., treating 0.023 as 0.00002) which distorts the ratio. Final Answer 1/8

Question 10

Write 101/27 in decimal form.

Accepted Answer

3.740740…

Question 11

51.3 + 7.078 +1.38 + 0.9 =?

Accepted Answer

51.300 + 7.078 + 1.380 + 0.900 = 60.658

Question 12

The product of 3.5413 x 2.1 is

Accepted Answer

For the product of 3.5413 x 2.1 Consider 35413 x 21 = 743673 Total decimal places = 4 + 1 ∴ 3.5413 x 2.1=7.43673

Question 13

[( 3.242 x 14 ) / 100] =?

Accepted Answer

Multiplying 3.242 x 14=4.5388 Now divide 4.5388 by 100 So, 4.5388 ÷ 100= 0.045388 ∴ Shift the decimal two places to the left as 100

Question 14

9.724 ÷ 100 =?

Accepted Answer

9.724 ÷ 100 = 0.09724 Shift decimal two palaces to the left. i.e 100

Question 15

5 x 0.25 x 6.301 x 0.00394=?

Accepted Answer

Here 5 x 25 x 6301 x 394=310324250 Total decimal places = (2+3+5) = 10 ∴ 5 x 0.25 x 6.301 x 0.00394 = 0.0310324250

Question 16

0.8 x? =0.0004

Accepted Answer

Let 0.8y = 0.0004 Then,y = 0.0004 / 0.8 = 0.004 / 8 = .0005

Question 17

0.9 x 0.008=?

Accepted Answer

∵ 9 x 8=72 ∴ 0.09 x 0.008 = 0.00072 (Five place of decimal )

Question 18

Solve the following: ? % of 10.8 =32.4

Accepted Answer

Let k % of 10.8=32.4 ⇒ (k x 10.8) / 100 = 32.4 ⇒ k = (32.4 x 100 )/10.8 = 300

Question 19

Solve the following: ? / .0025 = 800

Accepted Answer

Let k / .0025=800 Then, k = 800 x .0025 = ( 800 x 25 ) / 10000 = 2

Question 20

Solve the following: 0.001 /? = 0.01

Accepted Answer

Let 0.001 / x = 0.01 Then , x = 0.001 / 0.01 = 0.001 / 0.010 = 1 / 10 = 0.1

Decimal Fraction Questions