No of steps S= 30x+26 =18x+34 (where x=speed of escalator in steps/sec)
solving above equation we get x=2/3 step/sec
hence number of steps = 30*2/3 + 26 =46
2. Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is–
LCM of 5, 6, 7, 8 = 840
then (840x + 3)/9
if x = 2
then the number is divisible by 9
= 840x + 3
= 840×2 + 3 = 1683
the sum of digit = 18
3. Fifteen years ago, the ages of the members of a joint family of eight people added up to 223 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. Find the current average age of this eight-member joint family?
a) 26 years
b) 30 years
c) 28 years
d) 32 years
Fifteen years ago, the total age of the family is 223 years.
Twelve years ago, (Just before the death of the first person), the total age of the family would have been 223+8*3 = 223+24 = 247.
After the death of one member and the birth of a child, the total age is 187 years.
Nine years ago, after the death of one member and birth of another child, the total age of the family is 187+24-60 = 151 years.
The current total age of the family is = 8×9 + 151 = 223 years
The average age is 223/8 = 27.875 years = 28 years (approx)
4. Two bikers A and B start and ride at 75 km/hr and 60 km/hr respectively towards each other. They meet after 20 minutes. How far (in km) were they from each other when they started?
a) 48 km
b) 30 km
c) 45 km
d) 60 km
Let the distance = D km
D = (75 + 60) × 20/60
D = 45 km
5. A & B are two partners start a business by investing a capital Rs.25,000 and Rs.35000 and decide to share their profit according to their capital. But C joins the business on a condition that they will distribute the profit equally (1:1:1) and for that C gives 2,20,000 to A & B. Find in which ratio A & B will distribute that amount?
a) 1 : 3
b) 2 : 3
c) 3 : 2
d) 3 : 1
Ratio of shares of A and B = 25000:35000 = 5:7
The ratio of profits between A and B = 5:7
Total profit = 5x+7x = 12x
Now, C joins them and the profit will be distributed equally in the ratio of 1:1:1
=> Each will now get the profit of 4x.
Profit ratio will be same as the amount they invested
In 4x profit of c , A will give its x profit and B will give its 3x profit to C so that each will get equal profit of 4x.
so, clearly, as A and B have given their profit to C in 1:3 so the amount given by C will also be distributed between A and B in same ratio that is 1:3
6. The vehicle of Mr. Sunil needs 30% more fuel at the speed of 75 kmph than it needs at the speed of 50 kmph. At a speed of 50 kmph, Mr. Sunil can go to a distance of 195 kms. At a speed of 75 kmph, what distance he will travel?
a) 175 km
b) 100 km
c) 150 km
d) 75 km
At 50 kmph, 195 kms can be covered.
According to given conditions, 1.3 times the fuel will be required at 75 kmph.
Hence, the distance travelled will be = 195/1.3 = 150 km
7. A student gets an aggregate of 60% marks in five subjects in the ratio 10:9:8:7:6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the exam?
Let maximum marks be 100
Hence his average = 60
Let his marks be 10x, 9x, 8x, 7x, 6x respectively in 5 subjects
i.e. 10x+ 9x+ 8x+ 7x+ 6x = 60% of 5 × 100
40x = 60/100 × 500
x = 7.5 …… (i)
His marks were 75. 67.5, 60, 52.5, 45
Since passing marks are 50
He passed in 4 subjects
8. A person can row 9 km/hr. in still water, it takes him twice as long as to row up at row down. Find the rate of stream of the river.
a) 7.5 km/hr
b) 4.5 km/hr
c) 3 km/hr
d) 1.5 km/hr
Let the rate of Stream = x km/hr
Downstream speed of the man = ( 9 + x ) km/hr
Upstream speed of the man = ( 9 – x ) km/hr
According to the question:-
(9 + x)/(9 − x) = 2/1
9 + x = 18 – 2x
3x = 9
x = 9/3 = 3 km/hr
Speed of the stream = 3 km/hr
9. Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the smaller number.
Let the numbers be 7x and 11x respectively.
∴ (7x + 7)/(11x + 7) = 23
∴22x + 14 = 21x + 21 → x = 7
∴Smaller number = 7x = 7 × 7 = 49
10. A man invest Rs. 5000 for 3 year at 5% P.A. compound interest yearly. Income tax at the rate of 20% in the interest earned is deducted at the end of each year/ Find the amound at the end of the third year.
Let amount = 100
So interest of 1 year = 5
So amount at the end of 1 year = 104
So amount at the end of 3 yr. = 104/100 × 104/100 × 104/100 × 5000 = 5624.32
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