Question

priya read 3/8 pages of the book in one day and 2/5 of the remaining the next day and if 156 pages were still left . how many pages do the book contain​

Answer 1

let the total no of pages be x.
the no of pages read on 1st day = 3/8x
no. of pages left = 5/8x
no of pages read on next day = 5/8x × 2/5 = 1/4x
A/q
3/8x + 1/4x +156 = x
x - 3/8x - 1/4x = 156
(8x-3x-2x)/8 =156
3x/8 = 156
x= 156×8/3
x = 416

Answer 2

Total number of pages in the book = 416

Given :

Priya read 3/8 pages of the book in one day and 2/5 of the remaining the next day and 156 pages were still left

To find :

Total number of pages in the book

Solution :

Step 1 of 2 :

Form the equation to find the total number of pages in the book

Let total number of pages in the book = n

Since Priya read 3/8 pages of the book in one day

∴ Number of pages Priya read in one day = 3n/8

Now , remaining number of pages

= n - 3n/8

= (8n - 3n)/8

= 5n/8

Next day Priya read 2/5 of the remaining

∴ Number of pages Priya read in next day

= 2/5 × 5n/8

= 2n/8

= n/4

Now it is given that 156 pages were still left

So by the given condition

$\displaystyle \sf \frac{3n}{8} + \frac{n}{4} + 156 = n$

Step 2 of 2 :

Calculate total number of pages in the book

$\displaystyle \sf \frac{3n}{8} + \frac{n}{4} + 156 = n$

$\displaystyle \sf{ \implies }n - \frac{3n}{8} - \frac{n}{4} = 156$

$\displaystyle \sf{ \implies } \frac{8n - 3n - 2n}{8} = 156$

$\displaystyle \sf{ \implies } \frac{3n }{8} = 156$

$\displaystyle \sf{ \implies } n = 156 \times \frac{8}{3}$

$\displaystyle \sf{ \implies } n = 52 \times 8$

$\displaystyle \sf{ \implies }n = 416$

Hence total number of pages in the book = 416

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