Mathematical And Numerical Reasoning 2026 Njfp Job

To multiply a whole number by 100, you simply shift the decimal point two places to the right or append two zeros to the end of the number. The decimal '.0' does not change the value of the multiplier. The calculation is as follows: \[ 999 \times 100 = 99,900 \] This follows the basic powers-of-ten multiplication rule.

To solve this, we first find the distance the car covers per litre (fuel efficiency):\[ \text{Fuel efficiency} = \frac{540 \text{ km}}{18 \text{ litres}} = 30 \text{ km/litre} \]Now, we calculate the distance for 16 litres:\[ \text{Distance} = 30 \text{ km/litre} \times 16 \text{ litres} = 480 \text{ km} \]Note: The provided answer B (223 km) is mathematically incorrect. The correct calculation yields 480 km.

First, find the total pay per day for the group of 4 workers:\[ \frac{160,000}{5 \text{ days}} = 32,000 \text{ per day for 4 workers} \]Next, find the pay for one worker per day:\[ \frac{32,000}{4 \text{ workers}} = 8,000 \text{ per worker per day} \]Finally, calculate the pay for 5 workers for one day:\[ 8,000 \times 5 = 40,000 \]

Distance is calculated by multiplying speed by time. First, convert the mixed fraction time to a decimal or improper fraction:\[ 1 \frac{1}{4} \text{ hours} = 1.25 \text{ hours} \text{ or } \frac{5}{4} \text{ hours} \]Using the formula:\[ \text{Distance} = \text{Speed} \times \text{Time} \]\[ \text{Distance} = 80 \text{ km/hr} \times 1.25 \text{ hr} = 100 \text{ km} \]

To find the percentage profit, we follow these steps:
1. Calculate Total Cost Price (CP):\[ CP = 200 \text{ bulbs} \times \text{₦}10 = \text{₦}2,000 \]2. Calculate the number of bulbs sold:\[ 200 - 5 = 195 \text{ bulbs} \]3. Calculate Total Selling Price (SP):\[ SP = 195 \text{ bulbs} \times \text{₦}12 = \text{₦}2,340 \]4. Calculate the Profit:\[ \text{Profit} = SP - CP = 2,340 - 2,000 = \text{₦}340 \]5. Calculate Profit Percentage:\[ \text{Profit \%} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]\[ \text{Profit \%} = \left( \frac{340}{2000} \right) \times 100 = 17\% \]

Step 1: Find the Cost Price (CP). A 20% loss means the selling price is 80% of the CP:\[ 0.80 \times CP = 3,200 \]\[ CP = \frac{3,200}{0.80} = \text{₦}4,000 \]Step 2: Find the target Selling Price (SP) for a 20% profit. This means the SP should be 120% of the CP:\[ \text{Target SP} = 1.20 \times 4,000 \]\[ \text{Target SP} = \text{₦}4,800 \]

To find a number that is divisible by a set of numbers, we first find their Least Common Multiple (LCM).
Prime factorisation:
\( 21 = 3 \times 7 \)
\( 28 = 2^2 \times 7 \)
\( 36 = 2^2 \times 3^2 \)
\( 45 = 3^2 \times 5 \)

The LCM is the product of the highest power of each prime factor:\[ LCM = 2^2 \times 3^2 \times 5 \times 7 = 4 \times 9 \times 5 \times 7 = 1,260 \]The problem states that the required number, when 'diminished by 3', becomes divisible by these numbers. This means our number \( x \) satisfies:\[ x - 3 = 1,260 \]\[ x = 1,260 + 3 = 1,263 \]

Let the radius of the base be \( r \). Since they have the same height and stand on the same base as the hemisphere, the height \( h \) must equal the radius \( r \).
1. Volume of Cone: \( V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^3 \)
2. Volume of Hemisphere: \( V_2 = \frac{2}{3} \pi r^3 \)
3. Volume of Cylinder: \( V_3 = \pi r^2 h = \pi r^3 \)

Taking the ratio:\[ V_1 : V_2 : V_3 = \frac{1}{3}\pi r^3 : \frac{2}{3}\pi r^3 : \pi r^3 \]Dividing through by \( \pi r^3 \):\[ \frac{1}{3} : \frac{2}{3} : 1 \]Multiplying by 3 to clear the fractions:\[ 1 : 2 : 3 \]Note: The provided key indicated B, but the standard derivation for Cone:Hemisphere:Cylinder volumes results in 1:2:3.

This is a geometric progression where each subsequent term is found by multiplying the previous term by a constant ratio (common ratio \( r \)).
Observe the terms:\[ 1 \div 2 = \frac{1}{2} \]\[ \frac{1}{2} \div 1 = \frac{1}{2} \]\[ \frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times 2 = \frac{1}{2} \]The common ratio is \( \frac{1}{2} \). To find the next term:\[ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \]

To calculate the simple interest, we use the standard formula:\[ I = \frac{P \times R \times T}{100} \]Where:
\( P \) (Principal) = ₦5,000
\( R \) (Rate) = 4% per annum
\( T \) (Time) = 9 months. Since the rate is usually per annum, we must express time in years: \( \frac{9}{12} \) or \( 0.75 \) years.
Substituting the values into the formula:\[ I = \frac{5000 \times 4 \times 9}{100 \times 12} \]\[ I = \frac{180000}{1200} \]\[ I = 150 \]The total interest earned over the 9-month period is ₦150.