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Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q541.

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions ?

1)	24	2)	32
3)	36	4)	48
5)	None of these

Answer : 36
Explanation :

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels =³P₃ = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = ³P₃ = 3! = 6.

Total number of ways = (6 x 6) = 36.

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Q542.

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated ?

1)	6	2)	10
3)	12	4)	20
5)	None of thse

Answer : 20
Explanation :

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

So, required number of numbers = (1 x 5 x 4) = 20.

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Q543.

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together ?

1)	810	2)	1440
3)	2880	4)	50400
5)	57600

Answer : 50400
Explanation :

In the word 'CORPORATION', we consider the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO).

This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

Number of ways arranging these letters =7!/2! = 2520.

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5!/3!= 20 ways.

So, required number of ways = (2520 x 20) = 50400.

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Q544.

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together ?

1)	360	2)	480
3)	720	4)	1280
5)	None of these

Answer : 720
Explanation :

The word 'LEADING'' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

So, required number of ways = (120 x 6) = 720.

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Q545.

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done ?

1)	565	2)	664
3)	742	4)	756
5)	None of these

Answer : 756
Explanation :

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Q546.

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum ?

1)	Rs. 4462.50	2)	Rs. 8032.50
3)	Rs. 8900	4)	Rs. 8925
5)	None of these

Answer : Rs. 8925
Explanation :

Principal = (100 x 4016.25 ) / ( 9 x 5) = Rs. 8925.

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Q547.

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

1)	Rs. 650	2)	Rs. 690
3)	Rs. 698	4)	Rs. 700
5)	None of these

Answer : Rs. 698
Explanation :

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

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Q548.

A sum of Rs. 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs. 106, find the money lent at each rate ?

1)	Rs. 800	2)	Rs. 900
3)	Rs. 1100	4)	Rs. 870
5)	None of these

Answer : Rs. 900
Explanation :

Let the sum lent at 8% be Rs. x and that at 6% be

Rs. (1550 - x).

or (X x 8 x 1/100 ) + [ {(1500- X) x 6 x 1}/ 100 ] = 106

or 8 x + 9300 - 6 x = 10600

or 2 x = 1300

or x = 650

Money lent at 8% = Rs.650.

Money lent at 6% = Rs(1550 - 650) = Rs. 900

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Q549.

A sum was put at S.I. at certain rate for 5 years. Had it been put at 4% higher rate, it would have fetched Rs. 60 more. What was the sum ?

1)	Rs.280	2)	Rs.300
3)	Rs.320	4)	Rs.400
5)	None of these

Answer : Rs.300
Explanation :

Let Principal =P, Rate of Interest = R

Given, T = 5 So, (P x 5 x R) / 100

Now new rate of interest =( R+ 4) %

So, S.I. = {P x 5 x (R+ 5%) } / 100

Then, {P x 5 x (R+ 5%) } / 100 - (P x 5 x R) / 100 = 60

or P /60 = 5 or P= Rs. 300

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Q550.

Pipes A and B running together can fill a cistern in 6 min. If B takes 5 min more than A to fill the cistern, then the times in which B will fill the cistern separately will be respectively.

1)	12 min	2)	15 min
3)	18 min	4)	20 min
5)	None of these

Answer : 15 min
Explanation :

Let pipe A fills the cistern in x minutes.

Therefore, pipe B will fill the cistern in (x + 5) minutes.

1/x + 1/x+1 = 1/6

or x = 10

Hence pipe B can fill the cistern in 10 +5 = 15 min.

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Previous 1 2...52 53 545556 57 58...62 63 Next

Mathmetics

Q541.

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions ?

Q542.

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated ?

Q543.

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together ?

Q544.

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together ?

Q545.

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done ?

Q546.

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum ?

Q547.

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

Q548.

A sum of Rs. 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs. 106, find the money lent at each rate ?

Q549.

A sum was put at S.I. at certain rate for 5 years. Had it been put at 4% higher rate, it would have fetched Rs. 60 more. What was the sum ?

Q550.

Pipes A and B running together can fill a cistern in 6 min. If B takes 5 min more than A to fill the cistern, then the times in which B will fill the cistern separately will be respectively.

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